(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 283979, 5819] NotebookOptionsPosition[ 278995, 5649] NotebookOutlinePosition[ 279342, 5664] CellTagsIndexPosition[ 279299, 5661] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Bosons in a Double Well + Single Atom in 1 D Lattice", "Title", CellChangeTimes->{{3.472311465108655*^9, 3.472311486280655*^9}, 3.472312465542655*^9, {3.472312510293655*^9, 3.472312510412655*^9}}], Cell["Ulrich Schneider, Jan 2010", "Subsubtitle", CellChangeTimes->{{3.4723114953856544`*^9, 3.472311501591655*^9}}], Cell[CellGroupData[{ Cell["Bosons in a Double Well", "Section", CellChangeTimes->{{3.4723115110796547`*^9, 3.472311517646655*^9}, 3.472312465570655*^9, {3.4723125130136547`*^9, 3.4723125131006546`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"NAtom", "=", "8"}], ";"}], RowBox[{"(*", RowBox[{"Total", " ", "Atom", " ", "number"}], "*)"}]}]], "Input", CellChangeTimes->{ 3.4722953455505476`*^9, 3.4723013307592*^9, {3.472311527374655*^9, 3.472311543917655*^9}}], Cell[CellGroupData[{ Cell["Build Hamiltonian", "Subsection", CellChangeTimes->{{3.4722916532285137`*^9, 3.472291656456514*^9}, { 3.4723115623716545`*^9, 3.4723115660746546`*^9}}], Cell[CellGroupData[{ Cell["Calculate Matrix Elements", "Subsubsection", CellChangeTimes->{{3.470311527539431*^9, 3.470311534167094*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"tunnel", "[", RowBox[{"N_", ",", "i_", ",", "j_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"N", "+", RowBox[{ RowBox[{"(", RowBox[{"N", "-", "1"}], ")"}], "j"}], "-", SuperscriptBox["j", "2"]}], "]"}], RowBox[{"KroneckerDelta", "[", RowBox[{"i", ",", RowBox[{"j", "+", "1"}]}], "]"}]}], "+", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"N", "+", "1"}], ")"}], "j"}], "-", SuperscriptBox["j", "2"]}], "]"}], RowBox[{"KroneckerDelta", "[", RowBox[{"i", ",", RowBox[{"j", "-", "1"}]}], "]"}]}]}]}]], "Input", CellChangeTimes->{{3.472293376645232*^9, 3.4722935015262327`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"tunnel", "[", RowBox[{"5", ",", "n", ",", RowBox[{"n", "+", "1"}]}], "]"}], ",", RowBox[{"tunnel", "[", RowBox[{"5", ",", "n", ",", RowBox[{"n", "-", "1"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input", CellChangeTimes->{{3.4703098800274763`*^9, 3.470309954617934*^9}, { 3.4703100338848605`*^9, 3.4703100397254443`*^9}, {3.470311556650342*^9, 3.4703115632900057`*^9}, {3.472291788618514*^9, 3.472291826296514*^9}, { 3.472292099833514*^9, 3.472292111296514*^9}, {3.4722922132281494`*^9, 3.4722922432641554`*^9}, {3.472293593961232*^9, 3.4722936095362325`*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJw113k4Vd33APBz78UpTdzb4JVQKRlKGjWuFb2aDCmSDJkKKRqQShSVzENC JMlQhlSaozImhISQsUTIzMXlcr/7fZ7f7/xzns+zz7PP3mufs/baiy0dDxxj UhS1m0FR/91j3C1FVK0vbaf+78qvlNUylDUCt9/cnZrtDBR8+uAlK2sH/98+ O/TVU9HaszBkUXOj5S8DY7IDZIRlL4Dz6ZvKab0MVO6zDhTYeEA0n/HdZYCB jbPvTfFrPOFb2lsvHGbgyW3Op0ZlfCCy5nXPVx4Dn1e1JAxr+IPGsT8pEXwG jttrNQzYBIHldnkHUwEDd5aGLBupCYWzconT2oWYWDlhG9YvcwesX0tH/Z3D RJdC6dV9z6IgLO1wWAqbiZK3qkp6NO7CK9M1kbbzmGipiKy/NrEAUdc+/JRk omvajLeDNQ/ANKc45PMyJtL1v+R7ZJJh69E3GbZbmFib/d65uyMZcMDnosR2 JqYkReb9fZYCs/2LDxQiE3XO6hzt0kgDtZLtG5ZoMjF8+rvwPzZPoOyqTdWX /Uxk3/3MHKjJgPpjiz5zjzExrjj2zF+Zt0Bto7TvBDFxOPKlYrP/W3DSS9Ow CmWipk1J6zfeW9h/0l1F+TYTu1mjBu8q38HRxnMd76KYqLZNZ7OPdxYUOiR0 lyQy8esTPlO+7yNsOZ+WkJXJRI9i5b2qR/OgQG3dQH07E9Of+NSfXFUMJd0H whU2s9AGKu50n62ENXzDpi8lLHRoU2h9kV4H9QfWWv3REULRxdfkm9VaABnZ S2dUCGGgWIlinHkr+Kw7drUPhNGyXv8j60s7qBjqPz/wWBjPFFyzdJTvgsYn x53tZovgs9MzD0rs6YExzzz+FnMRjLtk37XasB92YZhE3RMR9Izl6w13D0DB Az/rwQERpCpbMOviEHQOqntoKdG43Om4q74iF5yVZ611tKBx5ebmg7GruSD7 wTlSwZLGddRhla4NXNjm99KvlVjdf0+7hwYXlhq3LTxkTaNZgrJ+qgkX3DNW /l5vQ2N41aAKM4gLgpc3FrWcpFF4vcefJ0NcmMzqv9h8nsbf3IhDM96PwP2P 14T8/Wl8sGPtuca8EbAKVz+zMYDGowFlQU+KR6DB4M2RX8Q/5ISLDtaOAF9x LH5DEI0VB89uuTs0ApZaArG6EBo/PNOSXak4CrMOZJkJR9AYcYrRpRMxCmGn 3Tj8+zTubTtxOfTMGBTyNy2wfk6j5uWlaTtdx6DeKuhiN7H6vIYfI+5joHHx k4XTCxo3/6utZuw/Bkx6ItPzJY2KiSpDSx+Oga3osft3XtM449iw7cuGMTiZ Z7L6aSaNX35f1q/dxYMoScWEK3k0fnbb4OWrwwOL1K23eMT5c/uebTUg7R+U 6LP5NGbtNJ8TZ8mDwISsyxYFNKYlqBfbXebBgfVOSZsLaQwgMZ3I4EHoIZfu 6mIadX4HK0lLjwOPI3TpaQV5n9LvKhO5cSi6dYDH/kbjvnMb3aMVx8FwfOcs Z+LdzKavEhvHYSVfYWRjJZmfrJILZ/84pM70+vKmisb1JgXZ0zzHobanPCip hkapKp7BUNs4vLoXHrqmkcaohdoC1e5xyIr/WeZN/I/V/UenB8dh6IxdXAPx /EHNiZ6pcYhi7ph+vYlGMbGw+x0LJkCyxef312YaWVqr/jbumYDpy6FU/xeN XXmWVz4/noADooNes/7QKBNSeyLwxQR0WgfFGxPrm+kY6GdOwF1/413JxB/G Nim2fJ6Aybm3Fmp00Bi6UrxqtHUCujmM0dOdNG6J+CgvL8mH4Ozyyy//0nja ej27R5YPdZfdf00QJ6mm8jPk+cAojy/Z0U3G9yW8Yvt6PmiKWyl9If5NOVw6 tJ8PzIcrFtf30Oh/Qqr8+g0+6Pkbd/7sozFnY+jbfQF8qD5nFiHbT+OI0LQE 8TA+zBOVKDYjNo8dco2J40Pf9g/v64jXVRUveZnFh+Ui25uKBmhs3HbB5fcg HzZzlOlbQzSuEv++SOPoJNjgdrGiERrbA9o9bx+bhGeCITUucYzo6J8/9pNg HhYzIjtK40whiQx/10nIM69efZ64a8RI83vIJKhsnR8nPUZjYkOjg13+JPxY nH3WiEejiVFvZWbxJHSGvf3rTjz3+5Ta7IpJCKn9zIsn9iyXYT1vnIQG39XV 3cTmuRYR/JFJ+HDayOfCOFn/R20fgxSmwON8Yof7BI1VciNyv1SmYBGr9nkM sV+ciO+6DVPQ8Xrr3Czi8Sh5/Tr1KcjsfRA2SlwbYNexxGQKltyaFWbHpzFY 9KK2s+UUmIfwp10n3uXtm1FoOwVexQqc+8SvrqS6nXSeglG/nX+qiG+d6xF7 FTgFqrZxgZsmyf/aP+k87fYU/Hv10WM9Yuap2fVHosnzV8Ys7IhPH1dJFDyc gj4ZV98IYh2jM5v25EzBn3kL6nuJRb5fvRddOAXp+TcSWFM0vj8QyuotnQLP +7tZEsTKWs9LQ39MwR2JwitALApci4ahKQiyKrnkQ+y6Y8W0V+NTkNLnbn6X uF3DOD2IIYCb18YL04lzd+eMq88RgM0OHZlvxKv3Dd+Xmi+ApNAVc1qJ72nL 7xqREoA8lF8dIr54IOBWsqIAJB5d72MLaOzQz97kpSqA0/sjuhYTHzIcajZR E0CT0gXb1cRrTIyUxTQF4C142r2P+O+xZQUuFgKoFJ624DLxEdvD9vttBaBr m7HiJvHnE37iio4CqNi29n0ocYLjgGmjG+n/6zuHJGL2WTmh114CSMnJ9XtC fMXJMCXYVwArAuOV3hCbXHg/ohEpAFbpwFAhcfGl/ruLYgWwe4O5VDmxmvtS jdFEAdy3TS6sJk66cqjza5oALL6UcuuJ53r5BKU8F8Cm3NKkn8Se17PWX3sn gFXxyT/aifu9++pNcwQQn20R8pfYzHeJ58bPAtC3HinuI/7ib7BCvFwAhl9t vIeINwfdLOuqFoAsvPo0QvwoJNMpv0EA51t/3uQRzw/rlbzXKgCvjq7SCeJr 4YtzzncJ4NOZituTxIOR+jZ6AyTe0bdbpojNo71nKY0J4JnrxnQBcVnMu+dC AgEsXvB66j9Lfx1R7mNSePDS3G//2UBPjDIRoTDoge6K/+z/TaHy83QKz3ja Mv7rL++gRtL6WRSOTTtqyicerzK58ECMwgtSa7eOE6sectGaM5fC+OjfMaPE tjVBMm4LKPQ0Pec5TBx7OHmwQ5JCN9Xmzn7i73W5BQbSFO5vlq/qJp5l3BCZ u5hCKXntHR3EOxu49irLKNTN0VFtJb5kOgfurqDwvZlyQiNxRtMK9nRlCgMe td2pIe48qt7mrEKhOl5kVxDL/jR+82sNhZkfO2cVEwe2BpplbaJQ4bVhwDvi AutHqgrbKLy71UA8g5jfliMUjhR+yleSSCY+0TGc4riLQnaCRfpt4ji72e4N eyl0Lfm4zY+4tkteb48OhbLhw7pXiHf1HBldYkDiZ9HMtyW+N9er0uMwhYV6 F76ZEA9vSX3SYEyh/H57lf3E930nbMItKfzsrO+x/r94yt+tnX6awjklcufH yf+zXzf/xfFzFObl23p3ESe5dAfnuVBoLzYl/YP4YMHWPZcvU7jmjcTv18Rp lo1v+30p/OE0UHCKmOkrHK4dSOEu43ixI8SHn608mxJC4e059379SyxMuSta R1JoJGEnJUVsFiMdXZNIoV3kmj+5JJ+I1R51+5BNrG9VyyP56rjA+/DCfPK9 vGBFNBFnLX+6zrWQwhyP7w25xHbOVI9qGYV7P82c8iHOZceZJtZTKHPZP5xN 7KT9a7v/CIWm1julZ5H8WewkurCTR2Hk6Y26XSQfy95dM/rvJIVbTIEuJC7t 8nwiYDEw/sL1mR7Ey28ulT0nzkBeZLp9J8nntbnWjCPKpD3m0sWHZH/o3/FD 8rIKAwNX7xz1IKZzdNfdX8PA07ZPRQ8Tb/i42aZdjYHvvO25IsRhmWKlZ/9l YNxt1R9HyX6j+yIr0s+MgUpOnOZJLpnv2jUZ6RYMLPPjFJQTu2c8LKmwZmBe 6a0dccRpT0OnFtgz0EB1xpQ6sehjW+uE82Q87cHXrg7T+Clx7ur3wQwMsswp 6BqksUnOd0/LLQa6MyPZr4i58QJLVgQDB0oLuFeI5R503d4Tw8A7bQs95hF7 3sueqE5moHyVVcwmsr9ujzhZ2JtLntdsEnYg+/XLm/lmslwG7ipYd8ab7P+P 9pZIeI8x0KtZYgCIo2Z++9YzwcDR6/rDo10k/wU3a2Yymahcl33tOLFW5Piq Q2JMHAro/7KN1Be/Hq4W+Ckx8alkykhVO42zC+/GjlowMVqjJiDxJ40Mn3gj M3KuUIsJctQhHt6bwimwZeJeX1bVSAuNdWWvvUMdyTnHb9oyTeKE798cV15m 4maL3vYmUi9tbp+GVpFMVHy2u22snsRX2LmlrIyJIkt848uqaZSUKaqZqGDi /BdJDx2Iy9QWla+oZuLrou5ts4k3nCx471nPRG5Ci6wWqedEKudFb+hgYnl2 5cdcUv8l3n9lcI/BwnUL1Eyjy0m9s2Ws+NQ6FvafU+3jfabR6uyllzOjWJgh +VDO/h3pb03TS4UYFv4THzs88Jas3yC+0rzPwrUPwo1ciZ+eEXl9JYmFvbuO //J6Q/LD6ZA3wxksrHzyvff2K1LvOz7MbCDnGnPvLT2JGTQWnazMSZtk4WZ+ 0X7nFBpVbJTKtCyE8JBGxdKvkWT97WQcH1sLoX1TxDEVYv+THLHZtkK4XVtX PpDU751nJvTKHYSwJsxGcW84jfFuJdV6bkJ4QktqVdYtGheE2jceihDCnzX2 S24G0ijISu02LxXCvQstz330orGcrTzDeZMwHpq1aVsyOX9kpntGK7NEcPVW bd7crSR/MhT3f2kUwfmNGv0rBSIo2nBxtwOp++OOHa78/E4E25IWh8W6TcO/ xm3p08+JYNiKf4TeGkzHzDUnjq+XEsHgqOOFFrKiGJRsO6CdK4xHwkzLZv4R xe/+eSIuFsI4tjORF/thBq7x2BzF7hXC1jZ111zvmegjdc13iasQPtimurDU Yhaaj2wt39HNwsfXncVtVs5G1SXaCY6mLPQ2sNrH4s7G1rk3dvTlM3F9Q1yy d+kcPPPyqkCKfKeRCtGPS/eJ4bJghaPrDRnokR0Que+tGM5bVfu+9CKF2gsN EovlxDF7xOZk/jwB7HAoNBb3EUetJWcPr5CbhFgpS7kvXHGcH1HYElowDnJ5 D8N1jNl4MHV44tP2MShTHktoMGGj7kLLfUvXjYFr+O7nJ8zY6PJvjN4FhTEo sessv2HBxmkRcyzYc8fgrJjS9I82bKyJvREz2jEKH03TL6k4sVFA76m+ETIK R8ZemIsFsHGZg269c+MIBK/MVfz2gY2fXyTWKphx4ZGa8XTPbDZazVC/F7Kf Cx81hv+o5rJRvN0wsFedC71GyxNDCtj4ylEsylueC/tu+MrofSHjzS4WWtc/ DCLNB+Z+rWNjlcJ2fUuPYbgU3DpZOszGXvM5TtZhQxAa7dZweYSN7Ldzvqtf H4KUpHmZK8dIfw16izguQ1Cbtcs1YIKNDvmR328aDsGGztRBLSYHzzTnrSn4 Zwj6dzj9KZnDQS93frRF9CAcHxKqKFLkYO+7H7+FQwfALGVnmYkyBz+ZLzo1 cXUADllcK+lbycHDCuF9zWcGQLOc9WmeKge3xYzLOesNwPJUZqbFRg6qZkv8 LZ4zAG2WVCJPg3h9kj33Zj9Yf5twVTDl4PjN/THyNb1g4rPFJcuMgxGmlsv6 nvWCPl46p2vOQSpSaek1/17YmT5+ytmKg2G6X4M5O3pBzpdnmWPHQcPkiZiM hz3QumNUy8iFg04N1yXXnugGy2eDsj5BHFSO32vUktUJJz0P8veGcPBh2z33 5b6d4HzwRc3MWxwUO1mnJTjUCTe5zoHB4Rys1Xh9xKyvA9I38SYiYjh4nvdc 1lOyA3g5gu9JqRxcGeFsZG/YDsxb5hm2jznoIPTCzEiqHWZa5wQoPiHxwtzm ey1tIC3itTM9g4MrAlw3S9q0wc69Ihkv33LQ+ESq3DL73xD8bWZAfiEHFRoC vF/u/gVR8adsbxRxcJLy038k+AnxTmUau0s4GPmg4pHly5/wan7weEkZB61l B9m9Uj+h4QjHtrKag0Wr6s/dftEM7UpOGrdrOPgoMflktWgz9PGrpA3rOBif 5x2radoEzNjw6h8NHFy9QNYimdsA8q3/aPxq5eB1FyV+SVcdrH5xUTqhjYNr XZyypv9TB5uv1/OO/eFg5/WQO+JYC1ryMU87uzh4lHlPaL3zdzg0NumX2s1B +9evm7derYajRWY2p3rJ/Pft/lt8tQrO2stKDwxw8FjUJu2Ow9/AbetVXsYQ B3Wtnn5SUayA67N+VTlxyfqp3y2KLSqHwCb1pxtGOSjtOJ1OEy6FyCfxfmNj ZL2gR1JjpAgeXBGyeTfOwTSvZf6pbp8gVe+Yuhufgx+ezjQSmOTCiyWfFm2f 4mDdp7onGry38GFoOU8g4ODg38nsnPg98D+if6gS "]]}, {Hue[0.9060679774997897, 0.6, 0.6], LineBox[CompressedData[" 1:eJwt13k0VV8bB/A7n+Oa4jZK7iWZ0qAJif2gUqhQGvxIyFAqEVGUUhkihFDK kCJDSqKkZJaxDKEMkblkykx5d2u995+zPmvde/bd++zn++wjaelgZE2jUCga VArl3/XBZUuW0nF3Dcr/P0V1PP1DvCPooXT0x6xbr9F8Se41Hu8EUt7ffpIw zUdCIVnP2U1OaNBK4QhHqxg9yLvFZfIuoI4V1Z6r/D8gxaHjgfO2nmgI0exa HCpQq1D037lGL1RyP+mzlmA1OqXucnqS64cuBMfJBB+uQRn17Y/GtANQgJJM ppF1LZqx128ZsQ1C+ekHX5+yqkPbq26vmmgMQXIpg/sK1T6julm7sGHuXaR4 V93V+WoTOl8qsX4o/R4ab+ltf6H5BYmF1lf80r6P3m1Yb6439wVZKgD9p20M ujEkSjG2bEZuqfzZo40PUeAgS8VjthURzd9lf3GTkMC0yd0O3Q7UlPfOZaAv CfU//Bw6HNiBkhMiC3+mJyN/GZOq0ZoOtNdpr/kP7VS03IPa8vfAdxTO9ya8 1/YZ2sb6clzfoBOJ3v9AG2l8gUZbKgXvS3WjWaGspLPbMtBirXUdU0e6UdfV eIPh2AyUurtte15wN8qyvRw9dOIl6hGlrIqd60YmGzdtHZzNRAk+899Fq3tQ XHmM409uNqo5ciL7mUkfGovMVPgWkI3Sw6zPWwb2oZ22FZ2109kIDcTnxeX3 oQH6pPGbujeocaXzn08y/UhFfe9WP5+3aPWMpbLqQD/69GyOJjv0HkURh1lc 65/Is1xRV8m8EHGrDEfVlg+iJ+mvZFLuFCKn08dUjmwfRLWRWvRVlYVoc+Xb RpXTg0ja9vDbpapFyKDz2pRW7iAqp19fS+EUIx1/UfX7ZkNosXqz6MeSEjRj vIQrtHsYpT3zaz61thwN6uxoCrcfQT9EfwToWpQji+m9uh3uI0j2vK6GXFg5 ajYq2CsWMIJit/HHdU6XI22TlOrDqSMopCzAxqS4Ag23+r4WGBhB5zuDRnRM q9CdI5Ws83ajKIa/4prIjk9IU30feeTgb2SLau4OONUhYmGe0JzAOKI8nHjT 7F+HXrlstX63bBxFMsRbyh/VIY9e6U0uMuPoQ5mNRFJDHVKKTfP8gMaR3IG5 h9Zb61FtbmXsvOM46rOTTW2jfkbhsrOU3PpxdDLkUu6n4AY05DAV3xE6gc50 y3e+TPuCLn6rULg0O4nYktdlv6m0o5Dzz6y5GTMocEGFQtyxTtRSlHjgz485 ZNl84D29sge9dXI7/0ZwHjkWX7d0kP2BpL8mh7FdKZB+VmD/0t2/kBixUHhY kwpx7vY/1h8aRieWj1GXsGngFTNnOIbX4aeqYv71lzSg1LXD24u/UZuwaG3t HjrIONu4HVAYR5rX7pxd00OHrvGIg/zvJtChyzrDe+wYoNt98lKI4xTan8o7 r9HPgL1dwaslJGaQ/kfeuK0pE34UWl758HQWqXjsXbktlwlrRRpWaJv/QUKd Y7tdJVjARuMWLb//IjUIV3ZxYIHOL5NJKWMKTDxvrGHksqCp4DjVRJEKF7pa 926kEZDpW3SUN04FSpxw6KKtBNgwXdqrq2mwfp9ZnOcZAsS4ZY2zNTRwXr0p YKMDAdUqKz7KfabB69OX6b3YW04Vv/NqpkF6WHiEviMBrLpFUVv6aGBZPH5Q 1JmAx7FZxtFUOkynH1bzvUBAl9pU+elNdLCWO9a+4joBVk7umQL36HBHp/3Z aAS+34a2TPkHdCgWjBHwiSSAPQpZO2PpwJMMnRO7S8BzR9arKwl0kOOphWve I2Du7O3XYy/oMBdrl+53n4Bwh8Sclgo6hNEWBTLjCCg7VZef+ocOWzU2L05N IuC+4paCMgoDDKru9m1IJuDsQGRBD50B/cky+7KxF586WshjMyB5/nNTUQoB lvb9RWGLGbDulNG3hqd4vBPzpR7rGHDbpC+3J52Adbarq/UtGGB94fRUZjYB bSe4Dk+PM4C1Qu+x6hsCAk5xFgjh5yqeoF7/Frvfcdbw4xkGlFO8XufnEBDv UfHZ0IMBktIno4rfEbAkxL71YAQDzJPTajLzCZh/mzJwrIoB72NoW1TKCEh7 H3Mr/xMDNH4lbErFNi0IXStVz4B9nw5kccsJyC51P9v5lQHb3vdrMSsIOFer N2bdh+ej/+5qeSUBvb0/Z0/SmfAgael99U8EfBRV5HdRZUKpvoVTSQMBGqdP 90dtY4Kbftka6UY8XmlaaQFiwn7DxZeuYgd6KF1fsJMJO1XPNW5tIkC/Z8uf FCMm6Dbmuz/5QkB5tubQd3smqGzo93ZoIaD42KE6g2gmJLFbS1M7CNiUE5nu GseEoaMCfH+wHy36GhT9iAnN+Rlt+t8JuF5uqj+QzIQcb3edn9hamyyLfV4x 4a6vlfDKLgLyiNOvcj8xgU7KeFzuISAnzStKkc4C97aSrq4feP/pG4tFsFhw zVvAaM1PAgz7Ze9S2SzIywnVdMHuXVkV3rCABfc83RLpAwRw7i4JuYLrZlHA oiCxXwTYX0v1rVdlwdq0AzXrhwjI4nkSSJ0FN29nHnfEpuYaeicBCzKVoi6m Y0dMTVy7rMOCPnPG2vXDBBSe1vSUM2aB+fs3GbIjBCw/3ODicZYFldIUjflR XF/jT8Z6zrHggojzrPJvAtJD3M8ZurLgEPuJ2llsnSqeo8xlFjz8brb9G/Y5 LftTn/zx/UvMXV+NEVChSLGSTmSBWmyEjcEE3q/ltR2BySyw/RVpeBXbwvbx semnLEAfbr1Px56M0z1a/ZIFOZNm0iKTBKxccueIWwELNLT6Rcqx3akKBpWt LHA0EPOUniagZzt/k0wHC4wKEpv1sQ18B8yvdrGAJvjlvTO2tPAzhy0/WfDZ dz23ELtSfFNQ7BQL3gj9VjWZIUBCRaPamYPXMSStw3GWAF937sGPi/G8wq9l h2CP5lLa5MUI2PhEYlkGdumOwl9tPAJ8bqY5jGKf3b9LcPdaXKdldhft5wgo OGOkv2I3AVFDFYTOHwIUX2ysd9XHz/VGg+kx7PDxhaa1+whI0C5QvYBt79Fo 73OQgClS2z8Je+FNU/8RK7wONQtuMf4ScLlKnaNvi+t0Wk9SDLtvATcq4SQB 29afU1+H/S6iI/k/nGMLM28KHsa2eWxTXnyZAGHBeYFH2J/6dIx4XgQMl+a0 Z2JvVZT/evEGnl/G6W2l2MIZP/vXBRBgLJPp34d9caLS8WYQAUNx+p5T2F2q adNdIXhem1tniHkCXued5buHc+0I/PJbhS3FMLo9hnPsodOZBxuxA3Q2LtsX S8CGTQMqmtgW1eNyjET8u8B24j9sdsvFXWdeEqC3NZ/ph73FNUkw6BXOkfUy KSH/vi/aVPsM546zr2xf1L/xdm02G8nD46tT5Z9id3VaSYkWEdDo/lUxE1vY M6R3Qynex22GH95i22QOOTpXEdB8T7ykHDvEQEL5Ds6NO8ln5Wqw3/3Un8us I2CH/nGpRuw+b/f8BpwjXVWTGS3YC6WSvSdxLixzW93agY3eNektbSVALXD+ QQ/2ycOEiGo7AXv2Ok/8wA7/vbnhSCcBtBG/nkHs/MDjURdxnb9OgjOj2APy ocei+vFzTIi8NY69tDh/1Vtcx6ILQrZPYWsfG/7RguuylW9N6Az2mVmJ539w 3c2kn7gwh30vfI+LBK6LtZK7Jv9gFyt5bEV4H4+c/CAwjz1cmTxvjvedzYMf 2f8sbvel6Aq+HstP+/vPu+jkzTgaCRZfFzb/87noLfsKmCRE9Ijv++doVeuF nSQJHW0lJn+xy+tDv9AFSKjMEv37b/wJh4JoaWESgk0pqrPYkvwjVjtESRDL DuKfxtZP4MrbLCJh/lmeywS2m+beQe+lJHhzQ11/Yz9q8chIXE5CfDtLZBj7 o2uK2wcJEiZLlmsNYM+IflXvlyShIbaG3Yctk0bS2atI2KYsZ9+Jbbhb+YOC HAmNe7hWbdgeXda39FaTQIvPGm3CrhMrXHJLiYTm3qKmSuy/mSMtTzeR8FhV bV0JtoIh72G1MglbAg1WvMe+4nNJcYEGCWZlB/OeYadKpY6s1yTBo3enSyJ2 47uvWYbbSTjvWp8fjb12TFkzVJcEd8kSyQBskyAb1ss92LvkN3th31C4U1Fv QILarGy7K3bLsVHjxYdIMOwcn7PAJud4y5VNSKDOFp45iL0xYl/7ITMSpK1W u+li36xKPXnXioTvaYWGSthZds3r3tiQoKz7W1Iau4POHv96ggS3x9l+i7FV ttp6ip/Fz+MTwZvB9dmdIBkW40HCBbhj+xZ74HrHNP0KCWGpU/7J2KOWceZ2 10io3XBzcyQ2hSu5WukmCaPcjUudsMUieAUFESRMt7kv52FLurTLykaRQLxY d4KNLbc/9pZ/NAkZdHLbGM6nzcK8Iwcek5D/gedYgm3gwx3ufkHCy6KKpdbY h6y/GetmkWCV4hGkh31UOyYnLZuEFfd3+iv9y7t5CR/XPBKqDnBF5/C+9XaV kOCrJqErNMvUH/ut7Qp9xX4S+N0nO//lb+GO1vTgARIMTE6n/Mvn8pUPlowP kZBX8W1yH3bjN/HOdxMkKGm/4PL/y+tD4hf3MfiANlGb7I7zXW7X8idOXD6Q 8F78dAeum3UyzYKNUnywQsqoUBx7CyPqnJoMH/Db2Rz9PYXrMU8MMdbwgc6o 0MoY7KMqYg13tvKBisXSnmHcf8LkljGyjfkgYckrg0u4Lk2PyiR2HuaDqS8d o/uwpcM26gqZ8kH36nB5KeyX83uCrSz5ILHp9oHicQLqG7zEhRz4oMc/OJaF zbkxsMnKlw9E1JyEXHD/DOl4by2YwweFMx/XUnF/NllSRark8sGBdo5ZCc4J qT1fUyzz+WBwvR/XH/vF67GRV6V84OQ/e4yDXRskf9myng/uySd8lhgkQEQj NPzVLz7YzVa5JolzJ/ieTakFjw38e7QbP/cS4Hre65zHSja83dk6Goh91Cia GyHDBsR2StDBVmQ3uFYqsuG72aXPr3CulV3YIaesygZ/oZdGod04945I+wkY sSFf52DJFpyDLku+6766xoaXoqPn17Xh9fn9Z6LGmw2h4g43m3GObv+4LH7A jw3R3babfbBFfQxnJYPZ4GieY9iKz19pE3kpAffZcN3cIf56M87nzzEClpls 0PWVTnyPz28mYWbVAr1scLO1FO6txXmXwV5u/4MNjTFjBZewv9W8si37xQYz y5IZDvZxYVGq9xgbSt8ITWrU4Hy9WbJxnsoPDfYekkEfCfC6su7uiDg/VCyc V16Kz5tJp6jHG4z4wYsSplaF+8zU9sfTMbn8oKeSQ83HfcsjJ+ZaUT4/LM6V y9TEpmy4J9hfxA+LbqvP5mcQQHCDJDdU8MMTN02U/wKfd6bddhc18kP4oaHH b57j+n+qf7dvmB8GN2T1Rqbi/7NoTEVppQCUja5h0x8R0Nmt5VbgIwBrpEsl Am7j82RM9UMFfwFo6+hW7gomIPawSVVIoACYIY1qNeyjFY5SVncEIOOvg1N/ IAFfn8dW0uMFgOHwMEID9/Va97+8HbkCYDJ8Qe+TN+6jIm/KSscE4Hv9Q/K2 O+7b6krLqywEQVpPbfMNfO54esNFxHaNEGh+Ytz6ux6fc4yt9OjjQlAvn5Gx AZ+bNrfEJflUCUN/yIC+8gsWRMpHPa3SWwBVrsxnhXYs8My7FamXvQCEmYl8 Q8Is2LPc+HG5tAiEez0PG0ljguaZ0v9E/ETAXDXn2U49JsSIW0pXjouA5NLq onD8XiBdmBi+9z9RuGBNqZf/jwHBawoUanNF4fb1ZkWnL3Sw+c2oKVPgQO/z xrJiRAfL9FGeXxAH8s/dDVoRT4NTXvvndG9zwOHxIFM7lgYu+182CoRygCpg Z2n7gAa+4y6BweEcuP/f+4rUCBqkqU7PRjzggHh0sqFCAA2m8+cbElI48C2S kzXkTIPgWoFbRaUcGLEZkYzdQYN78aftvMvw/cvaDsZp0SDeuVp7VwUHjBWS jsUhGmQtDp6pqObAi9obww9UadBiwrGr+8yBJlHOiO8aGsh2LtP+3smB7YuX jKxahN9bX16UeNTNAXr6rjULRWmw9UbztHUvByyKajdRhWmgL/vgef8PDjzO dYtvJGngZM+TGBnhQJZf3C+XOSp4bLs6/eI3B66SSudMpqlwQ/B7vfM4B06a LX2vPkGFyGfx/lNTHPDXskikDFPh4RWG7ZsZDkQ5XtRqH6BCiqG1lsccByxf mMTl9lPhpVTJCo2/eH1FTAujeqiQ+1tmen6eAzK9jYmunVT4H1sM5Sk= "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.470311549146592*^9, 3.470311565202197*^9}, 3.4703723929451103`*^9, {3.472291810778514*^9, 3.472291826984514*^9}, { 3.4722921011365137`*^9, 3.472292112336514*^9}, {3.4722922087282495`*^9, 3.472292244428388*^9}, 3.4722936103872323`*^9, 3.4722941336753626`*^9, { 3.4722953761326056`*^9, 3.4722953963036222`*^9}, 3.4722975602236*^9, 3.4723013361724*^9, 3.4723116349896545`*^9, 3.47231416323104*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"interaction", "[", RowBox[{"N_", ",", "n_"}], "]"}], ":=", RowBox[{ RowBox[{"n", " ", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}], " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"N", "-", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"N", "-", "n", "-", "1"}], ")"}]}]}]}]], "Input", CellChangeTimes->{{3.4703101493854094`*^9, 3.4703101510085716`*^9}, { 3.4703101886263328`*^9, 3.4703102359570656`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"interaction", "[", RowBox[{"5", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470310902407045*^9, 3.4703109400542793`*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwt2Hk8VO37B/CZOWfGEoWptHBmlOwJ45FKzYf2UiFa9DyEFFmzlEoRbSrx lKJEkhaRSkVKZLKLelJSqSwhQlL28Lu/r9fvr3m9X+eeOffc13Vf132OmrOP jSuHxWIpsVms/30mHHTmGW7bv8jJqaFrbEyEwmqh5UbhZvH8/GXm/D8ijBXn hQuF7mIbbrCh5oAICc8iBVzhXrHlqg3frbpF8FwY6NUviBBvzC4rTKsXoXrY LaZbcEFcp5o+PqRABKmPjZqdglTxaRXH0fhwEa6UX971XZAjvlR/YM0dGREy 7kR89NQvF4fumCKqkDHCDvF/Fzr8qsVWroUO62cZwrtZu+lBxnvx9crNpzXW GUBW7bDmF9N6sVb+lfEJTfo4rVChc2Vrk9iirP6W8pbZcP5om0+9aBE3Rixr MijVxa6iw84+mu3ivD3Rk1zW6+Cer9z6KSs7xfXZ5bN7x2njyn6PdoON3eLg aTZTlfI1EXb5j/Xvjp9iTvHZTNUEDbCq65G775d4yqk1bx1jZkEjYHuQrU6v 2C/j1bvBE+r42hu7YdzTPrH34GJe7Y2ZWNW888CZXQNiTu7X1azSGVj7NVqX YYbEbenLB+s5M9D+3Dm09PawuGSqhfciRzXoK9aoLnYcEattXZpT9VyIlsiW sHOuI+LdsxfXPiwQIkG2v7XVY0SsLz1skpgvhBw9JfNU0Ii4sDnuvt8TIdr7 Ni+r+XdEHGkemapzX4hrdZ+83QtHxLH7Nx2vSRZC5WZzfpT2qDh0MEiRCRdC VtzrVPdrVHxXpdHac7kQQeZa0llDo2Lfr3ELDywl91+8JSOKPSYu3JSVFLVY CMmKgiGLCWNi7eWzKh+JhdhnE3k2VWdMXD+/Ok/FVIjvrrOKdjuNieUO+nB1 tYV4ccpOS/HlmNjWP1XgJCfE/KjjVe1vx8RnKv8aSJIV4ua/TwIK68bE295o rWiUFuLwebWCPe1j4uetFmvduUIwr/r0fnBYaFx1ukVxRICa95IiO4YFpUGB uWqjAMs77ftn2LFgJVqmsCNDgMSJ4dUhm1gIS0oxWJ8mwO8FaXfqtrAQLJ2j bnFTgKQTwzvOO7NQWEod10oWYEjzUq2MLwsZsmoLlM8LkO78Kaf7BLnf2X3r gw8KoFDrGJz3jIXyJ6mWrtYCbB87tml6IQsth0qa0tYKkKtx1ziohFy3iF/b u1oA90BWp2EVC98ebLscvUwAidKVf659ZOGgfcjstgUCBKxpXHSqjwVeWvWw mqYAtZJtbHs9NuKcBrZmjjHoNv8w7cAcNs7MD1YMHmEgVbDOOMmIjd/mH+au GGZgkj9/R4spGz0f1Vta+xjEPFGo9FvKxgez36VLuhise5Abd9KBDdvM/TcC PjEovjbR4Gk0Gx0es0vTnzL4rH5iZf1ZNlhK/aKiJwx6r445U7FsHGy5OKk+ h4F6cvu5lQlsPJi2a75qFoOwxGfDb1PZkL27UfZhBoNFsZ4lXRI2nE/LP7dP YvDweKGDsJeMn6oSd/AIg5urKqYcG2DDQNvG+3k4g4tyr193DpP5+3dqjQtj EBr9ZdkTDgdWT9avvnqQgWXckP4GBQ7sFb8s6dvDoPGGwdhJXQ4kH7plNT0Y vHWfm9Ojz8HdxH2aF90ZlOou8t9sxEFjgruWghuD23dWt2rM40C4ds872pVB UPb2lwXLOOgItG5XcGQwvuTS5X4nDmoaWU331zNgR1zd7ODKgdGWz0vtbBj8 XnWLX+RGro9Xixy0YvC+KvvYGR8OejRrSletZZBS89pn9gEOQtXGfk9YyWB+ izRc4sjvG1oKZ4kZbOcG1ldVcSBd+lqybzaDaYKyd8P/cWC76XNOhB6DKlPV l1pvOXjmssEkXpfEz7PoadhHDrq/n8wv0mbAq54Ub/KNg8wCOf48DQbXkrLs EtkUCsNc8+IEDDY9ll1TQVNoLzSVe8UwkHvjsGRAioJBWNAXGeIAKSmRzXgK St4LJx9RYbDEe6MCbzoFs3GfCi9MZfB1wUC5lzEFlS3+GmYTGcTZWUouziVe N74ink/W3ycpp2Q+GZ83qXdEicGD5BU31cwpvJbf+b5MkcFhmQtH3q6h4Oyn 1RQygYHpzM5gjjUFK7Hm/V/jGXSYmQfMsaXw97Ez0juJbX3bnCPsKbw4nrHY QZ7k07t5WLiDgoL1n6Ft4xjUdkfO3bmTQkefQ1+HLINTso36sV4Uvirr79lD /HvhCdWf/hT0KxRlYmQYFKZ8GEoJpaDR3+X1XYrEN0+/579wCl2BD2OOEevV hrWNHqVQ7fMNGsQx43RrN0VS6H9zVtuDx8DFb/9DuYsUkrexzPhcsv5Gnx9q J1D4aXZ4ShHNQLYHWcuSKAx02TvtJb67i5cdep2CXj3LtI1iEG7onp2QSmGz 4FVRCvGGnxXZj9MpLDLtyXcm/uP776PfmRTm9OsPNnMYvDT4/Ugxi8KChJWm acTJ3Rty9HMojKpkN/kRr/RVeeyWTyE99USIDLGKQcjjIxIKsVndPrVssv9/ NDxOLqIwLyH1RSrxeZ8bT+oqKKT08yvWE7vPkc0drKLg5VHkqUds9sMzd/Jr sh6PyvZJESvceZkrekvWq17Y+5XFoMnb6KlVLYXJDeUfC4mz9M899fpIIe9J if4N4hNd/U9PfKag6qvcdZL4nwz7vBsNFIxHc6b6Ext4P80r/EqBs/3Ovb+J KX1hfkMrhYgb/Q9XENd0huWPtlMolpzRmEucers5f3oXhdzsUEqLONhrxTPT nxTcjxZYTideNzvtmd1vClX6dhxF4hmd8gV+/SS/7y5QlyHuS/ctiBoi85ML zKSIyzyrC9JHKKyyYN9mEV/SM5GUsWhEWtfz/2ffjjhJC0Xj+HylVjbx4vRh CSVFY8HIeQ0e8WRPh+dCWRrXLni/liNu0y14vlCeRsmEC+2TiHO/zyy0V6CR 5DjZR404Ku1o4R4+DcOIFsc5xM4ebYUxk2nsOyXzVEz8l65l0b2pxO4hR22I pb9nFFWp0DASrsjdQVx3S7H4u4BG8l0XhxDiOzsDiqVn0iib9trzAnGYzrvi WRo0bjqcbX1IvKF9XomFNg1x8I2qN8R/3MdKgufQOLuktGEqiedLbefSC0Y0 rH+8kQdxclthadZfNIr9ja+7Ea90P1HWvYDGO5mO6QXEKtqdZfJiGv7Tlwx2 /y+fvq0r17Eg/5f3w2ImybfzbpMqtq2gcW7nwulRxO5aQRWHVtNQaKpPLSU2 +/ahInEtDYu/3qXQJL8bdyS9qLWlUbk990s48ZwdulWWTjRCR93cL5P98tld 4HN7Gw2vkYjRHuJTnnyF8W40PO499lpJ9lvbrmHrl940Lpiu/jBKfDW44q11 MA3Jc62Ok2S/2oTk784MoWHiUWLdR8wKu6/MD6eRWxL4r4s0ycdj8ZvfRNAY usy+vIzUA+UzHp82xNJYUvm2R5/Uk+IYx4PZF2lAtUfrLnFA7HrBlEQaa2cw 84zlGPx3aYHT+xQaiauvtS4h9ejkjXHNWzJp8Kb7HjhO6tlYblrH1koasrf7 T8aR+piRfzmy4BWNyWsnuCyfxOBvyVn9GW9oGKeYTBwkzinZ79v0gcTX5wHt qszA//Xq367faFiGezKO0xi0tn4f3klx8SqhyrhOSNa7/culCh4XXVEN6Y/U SH3urF6oJ8uFylx6LHYGgys9T0I6Fbi4lRJk6KjOYMvIScqX4SLmj+rLCVok /kp64wLncRF32b5zcA7pv15ebfFmXCTbtmr1GJD5lmSUSMRclE9bUN9hyOB0 sOFhhWVc7P4wV9ImIvW9xWQkzYaLRZpH17NNGZTnmP9o9ODiTF9g2g2QfjYx vFLGh4ujT/2vlpgzuOVdmGbgx8XFc6bK7RYMImYudzsYROa7V9nPZCmDFZGW DVOPkPnJ6/R2kH5YtHVjtVUiFxaeyQb/kf5q/CTu3p4rXMxYqtg8xY70z0kf ohJTiOcsn+SygfST8r8tO25xEWwi3Ta6iYGFsXPRsWwukpS+/GPrwOCZlFd2 3isu0ln1wbtJv3+SERavR/Hw4r5+dOwh0i8t7abF8njYqjUwZEXOF9ZtmhfY sjzo65y1kifnj9aZledrFHgIfrsw9/RxBvwLymdCGR6+lrueexDFwCM8/fib eTzUGbDWnUpkMH1TTWCwLw+ebQ5fPPJIP++9+bvFnwdfrn1K2DMG987s97fe w0NGhobtJQmD5ZXCXRoHefh80zigtpjE38LD89VJHnhmM7P8XzKo0GO5qN/g 4eCnVeYmDQz2s3WsXnziQUG+MOA7T4CWJeNqNRp4OJX9eJKtjABWxzscD30l 1jp4NH+cAOoT7viYfOeBcfB4l6ggwAsV46ikAR6OK38xCZkmAGO6qCqALwW/ 57odxfrkfOltY6m6UgopY5sN/DYLIFu3b4X3AykEycgKTLMFMNmTKh+VLYUB nS5a8FgAJ6Xa13ceS8HiJO8f6acCPFrx1z8/n0nBWPqNS6OEnG8f/tgVUCmF S78aKu5XCVBwelv8vhYpbI8u475oEZDng7VdR6dIY6TbRcGdnOebr6vFXA6W xlG/Z3unWQjRcbhhkAqVxqN3UWacJUL0OF9xdAuXRvyhWJ/v5HmCJVDTNTwh jd1X12lIVgoxLVYokcRKY7/ApSbUWgirY4Lu5kxpFA1MNl/sJETuDlVLvTZp bDTIRN0hIWK0ptI5djLwu5/1zaFEiOiL20uchLIomcr6cmKTGuxj/qmSa5WF 9cJYFZshNQwsuTZ4OW8cdhpNnZKWPwNNzRZBkmNyuNmn62JxaiaSFxpOr3SS h4NLcdTfoeq4fSRQccfs8aDlZ6eb752FY3Yuq6ne8Ui/qMbvCNXAX3VXUo9V TgDvpnJm+wNNxGnH365crQDv2AlnuW1aCHkWGbc6RwHS2p8cd67RwZrpdtfK 1RWRZ7DtlrJEF+beJVsUIxRhJoq5PsloNi6rOKu/6FUE3vnFrnqnD/XnN86v 3aKE3F8mlnfmGyB6tkTndZ4SLG/S7R4TDLH9F/1fmQ4fBhPNf+qwjeB8r0cY EcWHc/Ct91SnETzD1v9Z9S8f5WcfBs39aYTA9Q/eyZ3lIy7Y6ZNHrxGO9wae jj7Ph5skvr9mxAgZ8waHYxP4qGcu+mSNF2GwYKzmehofKtPzvC4aiBD9Wi6y sISPD8KryX0BIly86uV2tIwPddfSXou9IlwNqFq8ooKPV/tOj48+IELW5Oih iio+tk0bidY7KkKdPd+t+i0ff+tse+8dK4Jm09TFjU18XIrcHDTlsQgGD/Yx Kc182Hw7OWtXngjzj3wcdG3lw2+iY1y5RARLzYS7be18fK1vrQqpEMHPQ8j8 /Em+vyo85FedCMFmhwYzf/Fx2iB3s02DCEfkG98E9JLxrecG7zWLEHfn6smB AT6Ky3VP+HeJkBxK73g8xIdtX+u+tz0ipFm7WgT/4WPZryWGpv0iPJhRrLpo lI/EAovb8cMi5P3SGBwb42Pr/78P+T8Zxy0D "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 8.}, Frame->True, PlotRange->{{0, 5}, {7.500000296179121, 19.999998979591854`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{ 3.4703115491765947`*^9, 3.470372393179097*^9, 3.472291839186514*^9, { 3.47229537617661*^9, 3.4722953963566275`*^9}, 3.4722975604108*^9, 3.4723013362192*^9, 3.472311635012655*^9, 3.472314163270052*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Build Matrices", "Subsubsection", CellChangeTimes->{{3.470310250758402*^9, 3.4703102631794014`*^9}, { 3.4703113498364067`*^9, 3.4703113512034063`*^9}}], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"JJ", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"tunnel", "[", RowBox[{"NAtom", ",", "i", ",", "j"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "NAtom"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "NAtom"}], "}"}]}], "]"}]}], ";"}], " ", RowBox[{"(*", RowBox[{"Tunnel", " ", "Matrix"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"UU", "=", RowBox[{"Table", "[", RowBox[{"0", ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "NAtom"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "NAtom"}], "}"}]}], "]"}]}], ";"}], " ", RowBox[{"(*", RowBox[{"Interaction", " ", "Matrix"}], "*)"}]}]}]], "Input", CellChangeTimes->{{3.4703106422237267`*^9, 3.470310750292258*^9}, { 3.470310964275407*^9, 3.470310965874407*^9}, {3.470311288544407*^9, 3.470311330006407*^9}, 3.4703150568436375`*^9, {3.4722935375172324`*^9, 3.472293545395232*^9}, 3.4722953878577776`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"JJ", "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.4722925717211733`*^9, 3.472292576815683*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", RowBox[{"2", " ", SqrtBox["2"]}], "0", "0", "0", "0", "0", "0", "0"}, { RowBox[{"2", " ", SqrtBox["2"]}], "0", SqrtBox["14"], "0", "0", "0", "0", "0", "0"}, {"0", SqrtBox["14"], "0", RowBox[{"3", " ", SqrtBox["2"]}], "0", "0", "0", "0", "0"}, {"0", "0", RowBox[{"3", " ", SqrtBox["2"]}], "0", RowBox[{"2", " ", SqrtBox["5"]}], "0", "0", "0", "0"}, {"0", "0", "0", RowBox[{"2", " ", SqrtBox["5"]}], "0", RowBox[{"2", " ", SqrtBox["5"]}], "0", "0", "0"}, {"0", "0", "0", "0", RowBox[{"2", " ", SqrtBox["5"]}], "0", RowBox[{"3", " ", SqrtBox["2"]}], "0", "0"}, {"0", "0", "0", "0", "0", RowBox[{"3", " ", SqrtBox["2"]}], "0", SqrtBox["14"], "0"}, {"0", "0", "0", "0", "0", "0", SqrtBox["14"], "0", RowBox[{"2", " ", SqrtBox["2"]}]}, {"0", "0", "0", "0", "0", "0", "0", RowBox[{"2", " ", SqrtBox["2"]}], "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.47229257788879*^9, 3.4722935500702324`*^9, {3.472295376212613*^9, 3.4722953963926315`*^9}, 3.4722975605355997`*^9, 3.4723013362504*^9, 3.4723116350346546`*^9, 3.472314163325068*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "1"}], ",", RowBox[{"i", "\[LessEqual]", RowBox[{"NAtom", "+", "1"}]}], ",", RowBox[{"i", "++"}], ",", RowBox[{ RowBox[{"UU", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], "=", RowBox[{"interaction", "[", RowBox[{"NAtom", ",", RowBox[{"i", "-", "1"}]}], "]"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"UU", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.4703107555807285`*^9, 3.47031085336395*^9}, { 3.4703109680754066`*^9, 3.4703109924094067`*^9}, {3.4703113419824066`*^9, 3.4703113740294065`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"56", "0", "0", "0", "0", "0", "0", "0", "0"}, {"0", "42", "0", "0", "0", "0", "0", "0", "0"}, {"0", "0", "32", "0", "0", "0", "0", "0", "0"}, {"0", "0", "0", "26", "0", "0", "0", "0", "0"}, {"0", "0", "0", "0", "24", "0", "0", "0", "0"}, {"0", "0", "0", "0", "0", "26", "0", "0", "0"}, {"0", "0", "0", "0", "0", "0", "32", "0", "0"}, {"0", "0", "0", "0", "0", "0", "0", "42", "0"}, {"0", "0", "0", "0", "0", "0", "0", "0", "56"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.4703115821898956`*^9, 3.470315060578637*^9, 3.470372396127327*^9, 3.472291847953514*^9, 3.472294188059306*^9, {3.472295376249617*^9, 3.4722953964286346`*^9}, 3.4722975605824003`*^9, 3.4723013362816*^9, 3.4723116350536547`*^9, 3.4723141633640795`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Hamiltonian", "Subsubsection", CellChangeTimes->{{3.472311604274655*^9, 3.4723116059616547`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"H", "[", RowBox[{"J_", ",", "U_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{"-", "J"}], "*", "JJ"}], "+", RowBox[{"U", "*", "UU"}]}]}]], "Input", CellChangeTimes->{{3.4703114324659247`*^9, 3.470311457260404*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["used routines", "Subsection", CellChangeTimes->{{3.4723116831666546`*^9, 3.4723116873816547`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"Energy", "[", RowBox[{"J_", ",", "U_"}], "]"}], ":=", RowBox[{"Sort", "[", RowBox[{"N", "[", RowBox[{"Eigenvalues", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], StyleBox["]", "Subsubsection"]}], StyleBox["]", "Subsubsection"]}]}], StyleBox[";", "Subsubsection"]}], StyleBox[" ", "Subsubsection"], StyleBox[ RowBox[{"(*", RowBox[{ "Calculate", " ", "the", " ", "Eigenenergies", " ", "of", " ", "the", " ", "Hamiltonian"}], "*)"}], "Subsubsection"]}]], "Input", CellChangeTimes->{{3.4703116528769636`*^9, 3.4703116824379196`*^9}, { 3.4723117277636547`*^9, 3.472311739851655*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"ff", "[", "k_", "]"}], ":=", RowBox[{"k", "/", RowBox[{"Norm", "[", "k", "]"}]}]}], ";"}], RowBox[{"(*", RowBox[{"Normailze", " ", "a", " ", "vector"}], "*)"}]}]], "Input", CellChangeTimes->{{3.4703127607705708`*^9, 3.470312812699955*^9}, { 3.4723117241076546`*^9, 3.4723117505136547`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Non-interacting case", "Subsection", CellChangeTimes->{{3.4703116334230185`*^9, 3.4703116406437407`*^9}, { 3.472311768823655*^9, 3.472311772726655*^9}}], Cell[CellGroupData[{ Cell["Eigenenergies", "Subsubsection", CellChangeTimes->{{3.472311784299655*^9, 3.4723117863436546`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Energy", "[", RowBox[{"J", ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"J", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{3.470311767115405*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwlz39M1HUYwHEIsHZg46BIRO6+x4cgTzBYs4kF34cfKh5wcXwkN1zUnfLD BBTGbQRURhDeHHQZKT9GDFEcY0AWZGRxT0gSAldKkQUtx3k5CDftuuSAIn2+ f7z3+vutMhzJyHnEzc0t7UEPbX3LsC764Im4FvLS0MiUkLpPOCSOkk2WtStD 7wrCG6L76EO7LK1Yp/QSTGILOWgpiDUW3lc2iYXkmGVqJb/hrrJL/IH8xfLo zFz4HeWgKDlvab/aVvynckzsJF2W3j7TTMHWX8VuUoZ54rWmxRKbeIj0xyL7 Zlt/77woGYgyVXX479vvir6kgPW+4+r21xxiA8nQMLPX4jHxj5hNhmHxt9WG I+HLYgmpxgtHffiGPf+KA2QktlccXoja5wZnySisalvV/b3oDtVkNLpN3YSv yj1A8jkMK80t26v2gqfJbXjLefpl76/XgZ18HjX21988WfwY7CS3o/aWeYtC IQMduQMXLhuOfdfjDYvkC7hVPh2c+Op6iCZjUSY69bOOx8GXjMPdd7Luh2T6 giTgjeGD7lkRcpgm43Hg+Ei24JSDZDzmehlvWq1+kEMm4IGSigGfZn8wkIn4 bN4Wa6r+CYgkk/B7vwhvY8yTMEnuxEu9VS0RHgFwkdyFFe7q9InfAqCc3IWy 2fLkov6nwI/cjfZOVUNb5QawkcnY8Eyg52BmIDSSe9DcnDuqFzbCSVKDWQ2v WH1ubwQ9qcGlpHOutqEgkExBmz2hbLh2E/xBpuKZ2OigSX0wNJNp2FNjlOdF KuAzUou1mQdSPJwKMJFa3Dbb3lU7qYRo8iVs3NzSM5kiQBOZjm9jXWPKoACS 6ZgWlHnuaqgKNKQO44tG98tNKkgiddi2yRA64VRBO6nD0MvnT2n3hwAjM9Ac Oay+PhQCkhmY6/C8NqZmIMnRcOEvwfQ+g2ySY0EVX9V8wECSo5H3/+zzIYMy kuNxp7HefIpBDcmxN8a1crqVQR/J0fXN2nRnN4MVkqP5uk/dyCiDepJjc0dh /ntjDD4iOXaUWhOTxxmcJzl+HmBeHrcy+ILkOJvlnz/1E4MbJMdwW2DinI1B KMkxqr9ccdbOIJLkuKNmxpVzm0EMyTE1vPWT+QUGWpJjyWFBce8eg6Mkx8oX 33F96mBQQXKsWT/3Y6nzwR/JsbGv48TSEoMmkuOZY555Xy4z+Jjk2K3LSahc ZdBFcuwPuRIc9x+DiyTHIUeYa22NgSTH/wFmIFbX "]], LineBox[CompressedData[" 1:eJwVjnk4lAkcgJUOiR63IcbwOWrcbZEc348RDT5PJbXpnHHu5og1HVKkA1vZ KRZprRxpyzrqmQ4q82uypDI9jsw8SC3ZHiI0TWZGrbV/vM/75/tacpO2Ri9U U1Oj5vnfpSe4S1yjzvnIB9tbrM8Jmlu6GSE7GD+QPb/TjvpKLwnnWptPMRhH SW/Dl1yatEJYihcsFjNyyYObb0rUpbeF8d68hBmLy6TeR+NLSolI2D0bVzBl cYMcfBia9FnSJVzaP2Q3YdFIBliPvZ6WDAnLn5Ulf7BoJxUS91+nJJ+EdfW5 /fFOfeRj1vWqzgp1jCU7L4+nDJMGbxr/4TpoY+LI6mFB3SipE7/v5lKWPmpa nrZ7s36KzHcNeBAaTsM8nefM8v0yUlrsgtM65sjt3yZUf/GFzKnKeLnQxBKT /zrNTbJTkYYFw7n5pQTeOqgVRmN/I7O2sX26vthg+bEDYy471OCQR/m+9qxV mFX2dcvn8QUQMKlKSxxmolr3W3iYpg7pXls4pusd0TY15sg25mIg6y4LTgid 8Z28aPvyR0sgSTGd+VTbFYNGfjx+KVkDFPY6g47hazD0Hd+eTtcEz5o/rxYW fodjT7iZT2uXw2e9oP3bRWvRSbfXnLVPG96d3789ZakbapJyzoBsBQROHmaP uLlj4ETEjFW4DoxGavwkyFiPUlHUgggHXQiwNl6YLfLAOzktexlyXdDvsM1r mNyAMYt5b8ViPTDKqd/s5uaFkSnH7miV6EORvYeOfqw3Osfai0M4BtBq6rtO dtEHX+o5LOd5GIK7mYjv3Evig7qsKw7qRqClXpHKyQI8toC5+cVrIzA/aeG1 09YXNQfSNiUKjEHDZvfdrW2+OFJtWVCWTgN7b5P6w3v8sGCVyaLGcBNIGtR7 EqTGQn5JTBuHYQrjsvPh7GIWRhTsEWu9N4WNzq0lbEd/VPhfU5Y1r4T7Ms/Z GbE/Do/4HRFlm0G8w5q+zuiNWOHturKDYw6eH6N6di4LwNozPN1YRzr4W9Mo 7YoAzA6PDFaX08Em8+cjIvdAXDdQfiO7wwJWRXsIbfoCsXj1ldqOYAZENced FiRvwgy8UBzcyIBHV3uipg3ZSK0Mv/bM2hIm/pibcb7HRt/Etl26uZbAsalZ VkIFYZkZ1/qF3BImmflut6eC0PrJ9cLQXVZwr2r2b3lOMPIdRcyuZiv43p8A T3oIxsgWdbYzCaAlZDc6YQhyb31i5P5CgIFm/C1qB4XxWWFfgy4SUMk6nja1 k0JemECilU+A0/E8Vv5uCnPkvDx+IQEhUw2vpBwK6zyUs0WlBOT0ypWR8RQq H8/1VtcQ8Kkiwy/tJIX8Lq0LLW0EDHjmd1fXUFhSmRB3tp2AGF7Vb+w6CitT xaxNzwlQ1d2JHm+g8K4RX/VcTIChlXTG9S6FAxH6cd2vCAjSMDd7hBTaDZuw hoYJaO6pjup+RaGLII1eNTL/s+K+4yEphRvO9Cuj3xMgCWz/QuunMMSutGF0 bP6n6UPO3rcUphxg0KenCbAvd6kdHaMw3euk8raMgId9vofOT1B4RnuoJ1U+ 3zMII52nKCyurzynUBDAyeZ1psoprMhcFNukIkCOZ0uMFRTWbIn2S/9KQLqq KLJJRaHAqtXc518C9NbecNjzjcJmma1ybo6A0oQm+dwchf8BZaVTag== "]], LineBox[CompressedData[" 1:eJwlzn1M1HUcwPGjAyrABlIkIHe/40uAx4NgaULC7wPftkzAZUhuuB7u5KkE DMZtBlREIN4cehrJg7ELSBtjHFmnG5V3n5AkBK4JZQ9Hy3EyB+qm0SWHFMnn +8d7r3/fGv2BlwsfUigUOQ9atfM9vW9ywZF0YZ9teErK3iO9KQuN9pVLtg8l 6R3Za2TVdnsnNqt9JKP8CdlrL00zlN1Tt8vCQfvU/ZKWO+peWThqf9g5E3Nb PSj7kr/Zuy6bK26qR2UzOWe3DBidpYm/y8Ile7F8pf1WpUsuIZVYPrvBZbXM yWXko+inaYj5c+sdWRiIRwPHtF1vLMjCYNQ7d9uV4//IOjIEK75v0B+IWZIr yTA8+3ZA7roX/5UtZAR21eyfT9qjgB5Swnrz8q6/b3mBUIOKqWvwbbUSViZX ZRhdVXRwt9YHhE/hdXfrK/4XfMFFRuOO2bfePVHxCAhjced1U5xK5QdCLc5f 1Nf90O8PN8k4TAy6GsFfXwObyAT0k9266YXHwJ9MxBdu59+LzAsEYRL+OlTg lR8fBMJkPHd4+DXJHQTnyWQs8jFcczjWgnAT7qusORfQEQwF5NO4sTjOka17 HITP4I9r4/0NKU+AcDN+Y6k/Fa8MAeEWrPHSvjT+RwhUk1vQb7p6e7n1SfAn n8XZM5oWc+06EG7FlthQ78G8UPiYTEFTR9GITgqDY2Qq5re86gi4EQbCVFx8 /rTHbAsH4XPoms08ONS0HmbIbdidlhw+oYuALjIN+xsNQcUJKugj07Epb1+W 0q2CBjIdN0939TZNqEEoY9uGU/0TWRIIAd/H5rasQQnqSMCc8LzTl6M0IMzA jPKRvUFGDQCZgeb1+qhxtwY+JTMw6uLnJ3fujYRoMhNNCUPaSVskHCczsWjB +8qoloGQo/7sX5LxGAMdybG0Pnd5x3EGQo6GXOsvAR8xqCI5HnYbjppOMjCS HC0pnvutnQwGSI6e71aunuljIORomgxoHh5hIOTY0VNWcmiUgZBjT5WDbx9j 0E1yPB9iWhpzMBBynM4PLpn6mYGT5BjjCuUzLgaxJMcka7Xqs1kGG0mOqY1O T+ENBkKO2TGdX8zNM8ghOVbul1R37zIQcqzd9oHnywUGQo6Na2Z+qnIzOERy bBvoObK4yKCV5Nhd51389dKDX5Jj367CzNplBhaSozXyUkT6fwy+IjnaFqI9 KysMLpAc/wdddFPw "]], LineBox[CompressedData[" 1:eJwlzn1M1HUcwPFDHioOGidJPMjd7/giJ8fj+V1bVvr7BG2ZPCxDcsOeODig RAjGbQpkSBDeHHoUQx5GFxA2ckAWttEDv09IEgJXilkGLsdxOlE37brkkCT9 /P547/XvW2ssfcW0RqFQZDzooZ0HjH6G/MNbPyE7RsZmhPRdwtui7H5p9czI B4KwX7xPWqRObNT4ChbxU7JNKt5i3ntX0ybK9kkz94qab2v6xAvksPTI7Lzu lmZYfIyckLrO2spuaCbEbvKSNDBomS1O/FPsJxelQvFc281yh1hEuqQSZ6xj aOC6WEp6JH9tne6vp2+Lsgo8EjSp73rLJR4lvdE4u1PynvpXzCf9sOynOmOp blmsIP3x5LsBWaEv/Sd+TQZiV9WexeRdCugmg7DWtrLjn5teIKtCxcwV+L7S G9aQwRhTUbBvp94XdOQ6XHAfe1X5gx9cJUNwu/Od9z4qexTSyVDMXLDGqdX+ kEGG4+JpY83P/Uq4QUZgoupiZOqbgZBERqK/6M6dcz0OSlKNL97KuRuVHQSy Av4xmu+VE6+CS6QWTx0ae0Nwq0BWiwW+5it2+1owkVGYV151KqA9GEwkw6TC OHt67hMgG42/rI1Xmjevg1/JDfjdQG1HvHcIyMZglZf+5anLIVBNxqD/XOW2 kqEnQUnq0Hlc22yrDoWr5EZs3hjmM5wdBi1kLFrbC8ZzhXBoIvWY0/y6PeBa OLxG6nHphV6PbSQCPGQcOpwp+0Yb1sMCGY/dWwwR07mR0EsmYH+9WVWYoIZB MhEbsvPSvN1qsJCJ+NRcV1/DtAY4mYStsR3902kCyCbj+9jYmjYsQA2ZjBkR 2b1no7WQThrw+ZLx3SqLFlJIA9rWG6On3FqQNWD06c9bMndHwQZyE1oTRvXn R6KgidyEBS6fcxN6BoUkR+PJvwXLUQZ5JMfi2qyV7U0MSkmO5qyh3wM+ZiDL 8ZDbfMTawkCW48Bmz71jnQxkOXp+XL14/AQDWY7W8wGNY+MMmkiO7T17iz6c YNBBcuypsKdum2Qgy/GbEOvypJ2BLMe5nOCimd8YXCY56hxhqfMOBrIck4cq 1Z85GRhIjs/Uz3pM1xg8S3JM13V+eX2RQSbJsXyPoL5zh4Esx+rnDnq+cjE4 QHKsD5y/UOFmUEdybB3sOby0xKCN5Nhd41P47fKDX5LjiR2mlOoVBl+QHIei zkRuvc9AluOIK8azuspAIjn+D9ckUVw= "]], LineBox[CompressedData[" 1:eJwkWndcT98bP+29CEnfyiyUkhBO7jWTQqiQVLLKSEhIfD5CQiUpKy1CKm0t hz7ttLS09957r/u75/7+6vV+Pc/zft7Pc8/nnPPc7lLLq0fOcQMAxEQAwH99 71vyrz/7fHsXRUzqH7b6mV6iqH9M0ZpQBmDNHfYmSGX+fqioeIfooYivET0n kC/HTYFP8SkxRpmXep6+gS5r37wyrvCOEAbg/d8OZ1gybeU1oPCNxhZ/wLqX UKC6SalXIZGOT16Yb/YGBeb4X+tW+IPxkKbjRxQe8bT68roqoptiufSXxKGu eV2u+09X0fGcWxNXsqCS/f7tyl5VxBrAlg5aFAbPVob082VVEXxA8nWPeBEM gCKBzZM4nhi77BWLavwvHUlRqSYWAk7bDZ9EuJgnj8ffvJroopLbQjVjkfF5 lR+OntgOuDdOR0PPP67nTTKqCbod6c+8s2GBSu8irQmM2Yvufs+DIh4H/ixY W0OoAlAatuAz3Df83WH4VA1hAoBRXZcHfGQsrlLkUUMsAmDqTVcc5CTa1Ian 1RDrAHg9oBkKZ+X+uruO1RCdFHXi68YYtJWtRl5cXUt8oqi2RYteI/vmF4M6 prUEPyDfOYcUwui9Ax9Xvqgl1ADoHIsJgP3fDAx5UmuJDop1foV9FFIRi+Jr HKklZAApgrZEQitbqfjfSnWEKGDbFNilwaCSa1YfTOpof+KzU1s0atxUvNjB DdstlkeczYTy7zVyj3HqiBGKiLNIy0Ums56OG4friIpJKmJFghF6bTGsOn9V PfbvZKmkwZK0o/UDx+uJdio5ROFWApJUivUoeF5PuIoC8NRCH+o/k94Z9rue yKdY0mhdCHLptRt+OsjgDdMFn5Bl8MXiDfMaCDEAHq5vSYOgSjb049oGoo1K XoMEEPIXyX0otYfB+tXHktDDlQXiVHUjMUSZT3b0/EEXiKJ3PdebiUFKYaxZ NQuBj2NJ1c+bCUnAkX73NB2+5ZWryQlqJgYo1p6u37lI/cKO2cRf2E7mek5k wew/5+W/lTUTVxvoBVJPIAsVV+JtP/ZXOHSjIh9NuEdZPBFsIUgAtFc5BkNl w5mP57ZizHYT1/oGOXFL0w2PthA7AFuCa2EgPL5Yp3XX5RZCEYBF05NJcODu Zf4Nj1uICepFRerKIuRS91JpmV8LzU98F/TKQYo74vdJxbcQSwHnaMfeGJjw qcYaFLYQgkA95rZqHTTg537e39FCSAHFVTbzMmGHlVJYHVcrsYgbaFpo34Hs XP38fNlWQowLzHNa6Apl1l3vQxtaiauCoOH0dVMY6fFGIky/lY63qDsdmUWv T6Tuc47B1XVKubDBqOnws/utxFMAXtVNvYW3EwRu3HnTSqziBpGLqq9DySWq XlaRrcQeAPYd3xIOv9078uPYn1ZiOSAtPovEw50Nt8r2NrUSQsDj19e5Sli1 03d843Qr0U/5/9zwPB9d/5wqs1K6jfZn87yqiIPCgh1bpFXbiFoq+fsNrWT0 8aLYSZ69bUQiRb0d9gxCW/M1HIfM2ohximj0N65HxWrHfRtvtRH7ADtiVPkT vOh573ehRxuxArBDbjyMgtyjH+uTv7UR8wBnelNiJnx/LBtEpGJM7ouNzIca Sb1L/arbCF0AelICwmGO3PxdbiNttF7b7rJDZdCSpXXWUaydxuzz3iKVcKrx 1ONLq9qJVwDchjc/QM/dD7+YEO20Hv/rvagIrf0anKV7vJ2oplj5P3mjULpQ QYfWtXailyKqG59lINPLw0LKz9oJPQD0rkYHwpECmbWLPmF+co/oUAl0Xb9d nx9hbBGeo1oGV3iduTJa2k7oA8C7X/8bRGMu7i297UQVxUpsvPgbGZ4Ijyjh 7yDmAyAvmsqBPT9LClMVOuj9L+BtumkZfCQ/ORil1UEcAEB9UXoYlHsgPz/w cAfWs/XesXwU27xL0+MijieVQUAa1N9rbcR62EEo0Vv85DoEW4Ld7W0+dND7 NTHnlFCCHEVi35z6wdi/9YomQ2mbygT9gg6ikmJdkuFNQt8L5yq3tXcQURS1 m1gThPZuWDG9BnTSesga+03VsM5bV052cSd9PrBPl2VHQ/sJG20hjU6an9ok 6lmKxE96mU3sZ+yZf77Ewi+/ElntZzqJCIqSvlMagrYr1geUOTI4yHksHJU5 8aZmeHcS0gAcrt6SDW1aVzfHhuN8DRphFRWwwaxSMOUPxgHBS+dXwaMVLuvy WzqJ/VzAtTr6Kcw8rGVYSXXS+z/F3341C2nltt9ple0ivgAAFZQ9YOjuN/6D G7uIBYD9pe8OB8r/3psxa9CF62m/HF8MPTaPdQld7iJGKf/w/w5WIJ6oz5IL n3TR5w3gNov6De3XGG1a9pHBLpo+SbDjE6/pul9d9PnA8dsZ+A+e/C/2wdaK Lnz+CHtkZ6KC12e+7h3GfMkuxdZliJScn39EvJtYC9jDz3cmw5inqUNmqzEG aadVouEqnusyl3Yz2GTzwt/wrePS7bfMu/H5s4QHlEHhscIzDx26icMUteTW cS907yr76Qvvbvr8Yu+usU6BAx1qET6R3UQpRRld3xmFLC3rS7/mMnj/h+OJ qLTafSqmrZvWY/4pyqcU6RhtV+Rw9dDxZOgT7TyYVNC7J0+uhzhAUdusLnsi lX2+lyo29xD6FPVgXoYf8kvRf9lypIc+3zg6+z6kQ6ltM3EDVxjMtUEqGz6K Da2ZcemhzzdWR+NkHhpTPcktFIQxdWCcl4OsvworL0juofMrCPO7FKIaxaQD S6t66Poadl7VqIAH31vfUB3toc8b8meLSilMmb/43RbJXhxfoLc+A2m6Zf/e s7aXzsfW9t+VCb/w3245vLcXn48vFlz7DRezlYTNTmN/1s9nxanIdbJM7aJj L82nKKd+uAjOXXc2sn+D/dmhr+nfw7WejXedonvp8xOUbXTNgi3nWgPc83uJ IorS/D0bg4zrvTLfd/QS5gCEqlSEwuzju3u+8PQRvLPUVdXA62hb8bBUjHwf YQFA5SNWBAzX+7Q5eUsfPn8Vz68pgooZR07lGvZhfud43UzIlxAV3PwM2xus Mk+UwK4QyZFpDsbk7Sj3Esiyd1166l0/fT6SKabLaqDw0kdK9VoDNLbQE4yr gNnwpdr9PRiT/3KVK6Dzcb/N/x0ZIGQBuVV+cw7cbRdKIDPG7n1EvB5yeyTo nLw0QExS9f125m2IE5pxaOoW9ueMRLfnwftZxcfePWLizbfm/4Gwud5c6+UA MUxRH/1XFaKpuZ4L5b4DRC5F/bH9G4cSZKeu2ocMEKUAJN3s84f2mwRuL4gf IP4B4Bcq+wZqHpFmx6YNEBsBeyrhZQIcurLU5Wghoyd6fXk5jHy6zmOoBmMg Nfq0HNp83vb2ZSfGAe4JsAqqpOwLUB8bIDYBtmv/rwTYXWMU/Jd7kGilkg89 +MlBIROWkTYSg0QORZWMhsYgK2nbBDG5QWIJYO93lfgDV6nf44QpY8xRnD+a Blv0nmXrbRwkxEGA5oHvxfDjhTeFXTswH8FXn5yHLB4GVTw9OEi0UKx9x6vy kLx/VIPySYyJp0V2f1BN0u+OrAuD9P2DOPT5STV6X5Y7cN5ukNg9Rx3a/MEJ HR+qmOB7MEjIAbZT6s9UuFC8DXx2GySWUpR39KgnKl09LLj7/SDd/+QOvboG 5LkHSDV/wXpA99q4ImhwWmyxUwzmr4+TXFSMxO/JLl3KYbDtgRUVKO+t0mpO HvYnF9jT6+NZrOZ688pBIouiNi+ejkH7CndsmWtl9Lfzvc1D/D0Hd/gODRLN 9Pl6P/ovShcw1YXUICEALMZS9Jug03Lrw9UiQzR/8puE4UJEEvYnHGQwpsRH 2cVozuTh6cUrh4j/ADD+cCYPInsP64T12G7uY1Ndghw8fa8d2z5E1/P3hZFd M9IKD7kztn+IsAOASDUIg2N/4h94H8Px5Kv4O3kwtjX9qebZIeImADKTjl/h da7ilyW2Q/T9jTru+181Uv+v/t31e0O0XtbZGKNM1KfVEyj1bIgwmKEkfPnu o++Gk98iXw8RTRRL84twKrpsyx996BOOr096caQcrXGdn9QXMURkUKwAdVYU 6viqmOqGhggJwL41fqQGfklTzVH5M0TIA074zec58Gz91uLcfzie9eVBVgla Nq1TdbEJ+zdY7VhbAhsWGjUJ9Q8R6RRrsutJDPLTsOwKnh4inlCU9s8735Dp watDOoLDOP9/do7FSPai41SbNMbmWZFPi1HF46fczksZu35vWTl6HfhaeOW6 YUKbvr8fv/oDGv76NC99K7ZTzuejCtG8ykjZMzrDRCPFst0zy0GFI7+WcRsO 03o4txTtSqC7ZO6aQIth4jFFRTRkB6DEzf/9OGgzTGwHwOzO6V+wxewqMXN3 mL5vRgTPn25Aks4pf749xXzJPCZC2Wjb9/mGx95ge/KBd08b0PnSc3W8n4eJ FIql0egcjzyn462io4cJBcD+/sg/A/5aJjxszsGYc/SOE33/1DW9J1YwTN9f qYp9bpWIeAs8rToxX7/EGu9G9Lot6Esa7wi+36qbZ9WjFLFx9WvzRmi72r2h rjbUo6n7U15xhL5/B1zxXlIIZUx99uSpjtD3ZU6vwvsMuOth79872zAGxdL3 cqFNCGGipDtCCPECAzUuR/i+6GVLqTHmq7ciJRpQxkSzjdPZESKZYlnKxiah AYVNk2rXcf7k6ec//yE5HZeHtawR4j5FGboafEE6NlViz91GiHqK9XpdVB66 7q3yVstnhFjMCwIytOyhH7q/rC14hL6Psxf+lM6Df5oLw17FYT5qWom3GI0I L9+8Ix3bQWKQSRpU1LiZ0lc0Qt93iV6NpXVI70SW3of6EXxfX60jWQLt2YvL dHsZ/CGFqxJ+/HrJYnxqhHCgqBmF8wEov+BXV5DgKLGbJojWPYkmRiVuHlk4 iu//jjIiTXD5f5YUtXyUWEbvZ8YvcuDB3bFPv68fpfOxjKqcy5HDJX7pk8Qo UUclH+WEZKHPnsf9BA+M4vu9umxNKSxMDFGOM8F8AcdyMpvhTMNM9BmrUfo+ W29926IBKQke0payZ/gvzm9Mg0fUArN+P8QYhAnszoH3jYcPX36J+RTd7x+t pu//e2oW+zP2uEGhHFga9OZ8VtgofZ+VDNyypAWCvM4BuyTsT/7uvVAK1w5v u7ssm4nvv/CuHBrLuvMV/hvF93/pbRdzkNOOhhf3mnE9xJtPD6vQdysN2bWD o4QrAOeSbL7BihePgirmsD9hZ7ojBfHGl61zFh0j+igWl2b/P6RWp5y4QXaM rudFaI1fEzLhu7urUQnbqReEaBlyVsnPd984Rs8fnMP2+9Nh1FGF43AX9k+2 +izdhGocrjV1GmD/+r9/x4uQ4Me0y2/MxoisWWr+jxwXtOHPgvHdl8eI/7hA 14FoP2g2cOHB0J0xev7gLN++JQs+W5QkEvCEybe3bX0t+rFd9PUB7zGihiLK y0EKajhnpjj9kfGvlbNMgaJukSHBkWN4ntm9/Fki3BzLvdH4N/ZnFUyW5yHL asNknjyMKSW+m3+RsE/jlWuVOJ691dEtD0ab2MjVt43heebDlEIUNJGdztEf wfn9VTlx9Yin6smdJK5xev5pCGbv/wfD3kkrK0uM0/MKZXrfikPPE4Fl3nLY Tspw51fBGZl1j3nWjON+bvm1vhAFVSRtuLYZY0rdUb0QjRwr9dA/wsQfHjuZ i/aU9/YqXRmn5wtW9p3QUtT32uGDt8M4nnfOyx2Lgq+NBfR4XMaJlQDYSoTn wu0LvSZtvcfxPLP06qF01PZPMbju4zg9j3A2PK2shu7e3431I8eJVQAYvvqR AjcZbeVL+jVOrydwkm9dA6yTzopRymXi11rvKUBPSo9aelcw/tmLfmVCda8G SZ62cXq+8M9bbNCAKo5eSbYdxvwkIdZYDtnzp67UgQkilqKKMu1jkXKJs5y+ +AQxTflbyukMokLP+bmJSybwfGL89kAjun0k4I7S6gn6/s9eKhjTDRXnqSp7 b5qg66X6wt/WoD9FiWXcuxl75j67Bnj95d7HtocniE1cYJ+S72soe7hkQ50Z 41/ZI12EUiUtmvQuTxB/5iidjK0v0cXCHo/EOxP0fMVOUK7+A+d53CGUnkwQ HrNUvfFKJ5R0iL/Py2sCzzvjC2yLoKXEqw/cH7E+/wDDJx1I5K+Cnm3EBH7f dsZKrAbFuodN1qIJPI9tClBH9Hm0JVgvZ4Ke1yi5ggUZiFc80zixfIKooFif 9edzUFj+ET6l1gniEADfrerioaFbfYzXEOZnWXim9aAZ/cuW3GASv1/rFZvt gEGik5K2YpO0Hs5r07vF8EDe4+Ra2Un8/o9/22Q+HHs+z0ZPeRLzu+/mzUN+ ev5yiRsnCQMAfjrM/IB7RVRyV+3CfBZhauxm2JeTcMfLgIlvI3gy4etne5S5 zSZxPbYKsyVo+/7isquXJonD9HzlLBkH24TMH9fexnbque9UFXrxp3uDnvMk rbf+XvhMI9J6ersp4dUksRqwrbMkUmHDPr6XqwIZvpRq+2LkIuhJeIUz+T9q 7GmF6tnyfVwI1wM4n58Xw8LMw8EJg5P0/MdpDPYog9cyHlleVZrCOCTU+x+U b9nLP7ZhCj/vtb5f22Aut1CIIzmF32+yfKab0e2luQd4DjD4ZGldD1pJug0+ PTFFlFHUtQ2CWajY7JC35HkGDy7wzkOse1Jb3lyfwvNipEBdOlT5UFLzH2uK OEZR8Zd+hqDKJG920HPGfm1neip0rjy2Yu3bKSKUXp/kyx9ow8Ti7KigKTzP GqeEVKKGhTWXtKIYHKVxrQi5bfSTSP41hefFvHiPXLjV0CJmTw4Tv9B4Ih61 X192LK9sivhHUaJiT1OQ18uWqSPNU3j+WuSY0Yp2RH7xq+xn+O5bF9WhvgKr nRYz2E4o9er1IJ/eNW1tgtP0fKYoVGXQDveJ9j69smAavy9t3ln9D46uiVAd WcpgpyKvIvhR91qRw7ppIpYbFHLnPYWHrDbc5NqG7aRov0ANnHEelXHRmSY+ 07+PVR0+6NvneCRuiPkDVjlrN0Dj9DsW3hbThAoAnzbR8yxP8zZeuSvTxDEA xL8mRMFIrrmvH+9gPvbxBKUSeEqRo7faeZrooljjCfJFSJhw6o/wZPRolr0v gvGndr/a5D9NGFDUyUrTQHTWkX/zr9Bp4jgAi/M2J0Apn+yqXQk4nlp3P6EQ /U58dj8nfZo4RFEZd8cj0KUK/WWHi7A+MufQqVYoMy6eWV7L5K9WtSuGGQuK rM26mPqKkGoFvK75Sqx1jMn/Va+9AiocNYq6xDOD8fcqxRKYd22R0ZDEDH7/ rPRm5T90x6Ny4rbcDJ7v56Z1G2FJ/inSeSP253RKC9RBVZGmJ68OYrvF2cXa TbDxcdfCcDbGDV832TZA96CwJE23GXreTY7mOV+BtqXZmP18x2D3myq1qKNR nXvnlxmimL5v57cWIG8w/Dk7eob4TFGpZq0I7VT4oXsoGfOBE0s4rbBf+1bv v9wZ/L5a/vmNv/CD6ZaXphVMfpmQLZ1Q9+60ZnML5icW/ne0FI29+1VhPTiD 33d/uNZWBD8lsBwHZmeIRABceMBnaFC+Q/GW8Cyex5HtlxI0O8qTPrtwFs/v y+VflcMQ6cwLj5Yz+EpYXgU8tsFFREQdY86Dbfx1kPfI/oiXkLHz5CSXwyhb 0aMyurPECK3/6MM2lPd+/p3vxoz/Zb+of7AtXdZ/51mcLzlwyetqBPqXZpRf w5jaVnaqFMkuXt19mTVL1PGBgUYfe6i5S12K220Wv08/rnelGB26snnzm/ez +P1AxKh3Frz4ZvsplWBsJ+yTZ8rQo5Q9D1N+YEyJO+wuQn7d+t+M07Ae/6Wy eztQwgLDv92Fs/h9weG9kXGwmDg5yq6bxfO+19rrTbDX2nLJwh7sb86OWt+G BL2sd4ROzjLvB5pKK+Gy37YXSIE52l6fc+lOO4Idt9z+Sc8RARTlotsVi4zn sWIuLpvD7xva88ZioC29Y1Bqc/j9xpeZqib47Lwb5aWN44nnDS6dKMjDa+Ua PYwVsn+FNaLkJB+95ONzhDqtz4s+T6taPl4zPD9H15Mc399RjUbEQ9503sB8 IDXkQjsU3xL16/4DjC1Q/sM2qHwmoXn+C8b/mAKnEu10Sxb69oHx15kP26Bp fKba9hDGPvjqUAWyb8w3KomfIyBF/bqWFIxeivy7a5WB9bDIR/29KGxjTeBs 8RyxGJDC2ieKYKZ5c5ZnA4PnnKRqYMPTrl6lPuzvH77kZCOaihmc/2sa29nm 4k6lULpuYssRIYr4S7Gkjj/PR+sEgUX7Qopop1iB58XK0T4NAWfHFfThCcDz e6FJ8IypeJiUBkVMUYeyNz0ZQPedFxR/ISjcr/z9Go3obaTcxLYDDC5QWtiE oquWyxeZUFiP4tjzUpjHu3b3eStsr7/b9F8jaluncXH6JkVoAGDATZ+P4MQW D4+HFDFMmZ//8LkJyT4k41a+xPEgWbS3Am78rlOT5Mf4c4L2/6F/Hwe5DcKw f/0qzaJmdJHLWLk1EWPimNSPbvRo7amDDlkMPt33th/5GZ21k/hHEfzAw+j9 g1GYwLr0PqiJInzoeWUPXzIq+Xads4UexjYA9qqO3r+wr+ROW8Eszs9R3xpR CnlZJH80HyBpPSvZ7aVQSnr3O0dRQOZTrEY7zl8k/01HRYe+TLVRyZ0jSv/Q 2u16yVKygKT7VdE9PYC0Sg4eqVHEdtYb6/gitMfqSOsXJUAOU/51L6lWdGTW 6Pa1dYAUAw2VHh8aobnnCRG4EduprfpPutBlpVN+/JCJX3nUuAjdQRbri3YC 8h29vjfcjkPOh8+m++gCUhZwArXel0OvtgvHzhsweiYffK9AgXcvdakfw/wk n+XjXqjOEZp4cgqQAsC26p/ZAOTwBvPVn8F29tfR0U5ooLt3/qaLgFSjqDQB uW+owa1F0c0WkHkUtar6XBayLXZa12KP+YnvJ3ZWIWrhUrjtHmOXd/2UjtxP Jut6PgTkRgC0fLT/QPmAU8c6nzL66/1sq1B4y/RZ0gOQb+h5XgXEIu3V76+/ eY392SOSjXkw74oWu+8DIF9TVMeLu3HINLrMbc8nQJYCMOHoFg57xux8PnwD ZC7F4ty+m4/ubpv/bTgCkK1U8gnlA7VImB0Vtz8OkBcB8Ax1i4bv0w+lByJA LgHspLn5VXCNUF/RRCrG5GdP3n8w8YBr/aE/TP8HPB064D7PNb1f/uL+NJy1 qRyBFWXZU7P/ALkJgM/vwzKg1ZILgkY1OJ4j0ri3Co6b8y0MawJkOBfo2XnL BzoHfVrO0wlIL4paWm/+Cy3s3LHepB+QH2eoeKceV/RFtWF71CiT313taQ3c eP2+vuAMIC8DsEisPRGmx8mZmHNzkUNU8tfSZ/3IcDrpQpwgFykOyF03Vftg C3HippgEF86/875eCbzxaNzp7AIu8gq9P+kMJEDuP94eP5cwON4rOg56imn6 zVuG/dk7tvjWwGVHikOtlbno+iw23eAZhFGvbRM567jIVxSlf58/EpHV4lmL NuJ8nHkOt9phocL3UpttGCtGp6m1Q4uzek0ZO7jIPxTrarZ5NuoP7uyX28dF TlKEQemLIXS/98nsjYPYn/048HgrFNdYJZJryEVuBuzbYbtyoZ99usyyk1yk HCDXXvT8B1V/Wq66c5qLbKEoHe7ZWoQooFl4gYvcM0fFt2W+Rfq7/Xco2WA7 0VnlU4hqXLQP3bfDOHmrTmgJupRfbfrPgYvUAuD9u2dZcErK4aLKA0bvWD/e 341lbj98wmDZrUfboKxP3OMqNyZf5kRHCfpWb/hqvRdj98jf1Qy1VgwHuLzH +tjSahOFMNvqZXh9AOZnmz0qyoDHv6uhTV9x/wzcjIwHYPtg/h+37/h5KSwW ofdb+02Xy1tiMF9D4nbfVsh/V7h1WxK2U5a3utrQ6+TgIU8Ok9/2ZEsZWsmr A7oyucgsimX8or0Axe5rFduRj/kblm4gRuFut4dL3pYw62GhwZ9eVFq0dHV/ JRNvJvqxFp1ZyNm0t4Hp56hzQTkcMjHb7dvGYOElyYXQyX/m8EgPF/kf4JiE q9VDA/WEa2uHMQYOgrbVUD7lxkvLSczPQgUXOlHPYbWodxSzPuTVakZgUlNX YSEfN15/o89kWqHLjS8DAqLcOH7w6mAxNOa1lCTmcZNbAbDxOsOBK7z/U7eX 4cZ833v5O9HQyspD3+W56fWhcNPi1QDixHldbVmB+QKkL9/pgu46Bi+WrMV2 CZcNG8aQaYVIxJH13GQmRVW3y6SjNdZZBU83M/y38y5kwIlJpz6ONjfZTCXH JItUosxn28UndmFMHDqfW4a8lkypqu3H8SxFmYX5yDLsx4HzBgx+eMY7C6lr X7via4z1czq+jpbDuXwVt1JTnJ+4zRoaR3lmHWEiZ7jJQcq/qYi3Eb3v/5S3 05qb/McFLptf8oFWbPOeO1e5SQlATj+52wc3SS0RjbqJ/Qlqf0s34v1Ytrbj LrYr/mz82QeLNTz1FJywPmq8UacMBaQduGTsgjHL0eVJNbIxFHru5o7jzXne LG9EsDU9JN2Lm2yikg1Lnen7uT07Z/o9NykPOCmPt9TBCn7YpRHIjZ/P7C2z IfjlzbjQxa/c5P4Z6mtRgguyU45ZHfgd2wNagvwG4I5EG92KGEZvg71vAxTf v8ZaIgnzU6sSHpWgmqpWl70cbvIWANVP+mJhyKXA4HuZ3GQ6RfELCeag2zOm 2bF5TH4fI1gM97rJdHQXM/VFHNveDKXlSwWWV3KTAwDU6XcEwqbwF0om9Qy+ +F93BIwk9HRetnKTEADVu3fz4P1C/gvZ3dykILCtf8wahfqnU52pQVw/aySz gT7/h+592TTBTboKAMWKaBbscNqSeWWOyefnad4O4+aPtgbx8pBPKOo04Ebo UVAkX40wD+Y7NvZ3BB7ZeHnlfCkecoJS2DLMGkGKmUp79i/ioeM5eXsDGmGf cfPZB//xkGkUJbh+Lh2hdr9HCcuxvYEdYNEKn902CepfzUProW5osNrRcaGF 6avUGX+5BY55aNX7ouZTmzC/hPxlhWE0ssaNxxtif/OHofJNKPXnvuV5OzH2 P3X/fjPy0OfdxaPLQ2oDtuZP5wJoVptsufUQzgcCqh+0QBWbu07XjHjIMQDs nyt+gVNzmz4Gn8T1sDNlU4Zg9ouhlPrTPKQCvf9n7C6DrxXDGxda4XiLGy+4 W+HZKGuugzZMfV/RxyaosXPl0sd2GLNZnaltEJQ0kMiBwXYLz/TAR52/Ax0e 8JCNFLExdaocCQFf7i0uPGQqxbp4+hZ9fi+8e2bcnYecBECUkg2A81RPpP/w xv7UihfaVejNrs0r7T7g+iNu+RMUkjNZ4KzxiYeUBAHHdS06YYDtcNvANx5y gEpWXwda0conRToRkTzkPQAsSqaSYIhvRPCVeMyXPG+r0z+0LtZNSOU3D9nL A8C/909gTM6li13pjN1R5lE10mrUzQ3OxfwW+o6+HRCNK6lcKOYheSlqfqxa MNohzu+2shL3qyFm78FhmLmipbe5nslv2MXTjfZvSz34sY2HVAScq3BzJSw4 HBBh0ctDEvT91qcnDR61ui+pMMJDsgBYfucfghX3Ta/VTvGQJAA/aztyoKn3 1mIfLl46nk2wN/yDDaEyG0wEeWl+8/vx/A3oXOrYKxkJXpJNzxdPMiNhV0Xp SNkC7E9yogcqoU1/tJG3HC/ZQCWbQoNSNMT3Mu7ocmwHEaU25fCW3NVF89bQ 8RSVcmHfTzSjceB2oTr2J5YKvapDbN21le6bcT5iavpbK+KzENp6YDvGrNQb Od3omX37e5E9vHT9FtbP1gxAcbeM6T96vLhfi31ju+GrT59MXY7wkskUpWkd kYtkkh782nsC5+dEmbaXwA+F5vJ8FpjP/9QflTa0tF2blXYexyuKJ0d3wi+z SxoeXOEldwBQoaCbBddIT5GkHbaT3IXXmmDEmorAOQdecikAOZEfy6Hmjjju Xw94yXoqeUzbrxglHPM6c9eF4T/3ur8JQZvr6Vte8JL8XEBagQqHKY8MVk54 Y/0G6r8uzMC9Puuc4z7geEplKrAW5USJttt9wvGUq11UEzqY3aWzIYSX/E2x Hkfq/EElddnBg5FYT4DJh/weeHz0i1BkPOO/rLq4BdWIPL5o8xvrI3+bvCuC FsvO5Kpk8JL9FGtDztFO1Kq1Q6U7F2P/tztGWtHFQwpu34p56fVNeZh2TaC+ c7O9Fyp5yccArHAwjoQ3HKsPrmrAfOxnEYY1cMIzMaKljbF7cx9KgI7f3kh+ 6sX1FN6MjR2CXJyb106P4HqIJfI21ci57GixwjQvKQXIgDtWTVC4d/2GOi4+ rKdwNr4FveCR9PogyEfbFfOffW2D0rJ9IyYSfOQuAF7oy+XAt+p5RosX8pHL AKdpc34h/E8nJK5cjo/OFyk979MU/HjKZdHr5ZhPwfaoSS9aZXf+tuEaPrKO 5vcerUOqW+uP+qtj/oY9LZxmqAmOq3Vt4iOH5qhhzqZgtC2zUHijNubjhCyt GYY7XXXbWLsYfpPJxCGoeyQ1JUeXj0QUtcV+Rz4ykNnmu8CA0a8WLt2FjtXF 3LYw5sP771lWzwAyC1IxDDVl9Jw59F87Onfxs9qYJR85Tv3N/as+iC6ry4vs sMb6qCcNemXoxtjrtudXGX1bkxc0QQckkVp2E9dL/q75WA8fOLn4LnXEGOhC 2RLoso/rzmUnBme+f1kBX4g7GMa7MPkuPZzuRa9Lh9S4X/CRPynWngNUAfJ9 f0nkgDe217cu521FQRYtbW98mP5IdnqUo9BVp1KbAhn87+niUhTd889XNZjh v1h6qgImRh+8czsc24me3DWViHM7yzAtlo9cDjhPPPXrYNZ2Ul38Jx9ZSxGh 4rAQFfAmipxI4SPtKSoXzYtB/3LWt3/KYvRpB6/qRTUeIal9+RibB01cbELN xsv9tpTi+jmecQZNsEvuw51HVZiPpaHZXowGm6SN/jZgf/8DXZtb0ESwm7ps O8bJPVtnmtGcDb/ouV6MibjnZDPi28hqjxjmI5Mo1rur8zlIdHo8dWoS81Hf jnuWoXkptn57AD/mt5iSrUCLn3Te8eDnJ9MEgeTGxbeg4gFLo2pRfnIvAKZP vuZCpfnV6qvm89PPr/7QZtUhtK7yqOi1xRj3PzKXmEQb/fPafypgvuRO+cwq BM/tSeNfxY/zn2b7ZqNda3/7HVbhJ/so8+rIS/T+PLjJ4YMGPzkPBFTO/W2C h+MjjNq1+MkbFDXr9jEeHb+nvF6D4CcTKeqSS1M6Mt8VKHpvD4N/5w7/ReeF ZDuy9PhJHcCOGppKhVf+eqbNO8JPrgBsq4qRSmjnLeJ/6jg/KccFbJNOf4J3 Tz5yCDbD+Ym7G90bkdPSWaPhs1i/ecPO1QPoafvN9dsvMXzzvgalQI/vfaJP r2EMfp59lQPf3LjQUXKLiRe7pdCC/LY0pMnfxzgZZJ/pR5+p4/7Wj5j6dskE t6KwjCKH2Gf8pBAwSM79Mwhjnu83pjxwvRxpnUNNMOlw2vr9bzAm9489a4Ep i6CYty8/WUMlf4u9Xo+ya2M76j9hPtZMyL0G9PeTavqaEMxH6nLXj8Ey6y/+ NyP5yYe8QIv7ijusVVO4y4nD9SgoHDw3iFpG3xiL/ML87Jx5gw3w444NN2rT MF+9dlNJGzJ3K3gRkcNPvgTg694tMVCu0jrsQRGjp3TDsj5YtYLvz9EKJj55 e20DfGsb0LqynsnfvsJ1GBqjbdwTrThf8jujshEkLVgun9PD9OdUwGAPKjp6 fduHYX5SF7AFQldmQXd/seM2U0x/bj6724H0u4PtSC4BMp7en2a4/iDhzbtf zhMUoP2BvWrXX5jtVP+9RVwA57/1emMjdC5wyIlbIECuBGDDrsZyuEt2YbuL HLaD2dDQRgjOR/GcXC5AxlFUt+K5AvQ7Sl9RdY0ArVdRsFFyFDrOtkNKXYDW S+m8k5pCW3QfnijaLEBGzVIKE7y+aMxL3v7TdgFyPwCtz/X+wtiGRM+bewTI XoqVIjXUgq6rGEXo6GO+hijHFQNQ7fZA7uKjjP97SUkO7El73tF9AutjW/13 /x8MkVDi+23BYGHNkRJodTJ1qccFAdIbABOlb7/gyq+ntlvaCJB6AIT+5qTA pqEJE82bAmQ1RV1+9q0SBWz3usXvyMRHP88rgmbP1LwqnJj6zQJ3FkK5spzI kKcMLolPqIRVS8/nO3ow8aIbisrRmytcXQffYP2UrbtqLzJM/MC/1I/BDx4O taJ5fFrLh4MEyPmAnf1kXzMsNCghMkIZPQL7xfOg+wcb0zfRDK6wn+JA/Q6h O9aJAmQVRaFw0RIkpPnZexsH8yXn6Od2oEwWGS2WhftrHqUoOIwe5VYX1OcL kPr0/X9VaCbcuehWd1Qp7h9HqWtoEFKW8wQfVeP85IX6APp+F/59hXET5md5 rd1Xhhym9u1Q7hQgYymqfU3QH6S1t+XUVD/2B6qguA2OvmQ55I0JkGP0fOmQ OICia2Xf+M0KkMIgQEMkaALaro6LseUVJN/R/eJbHAvX3TxcuFNEkIyhqLHD Aimom9PTIz1PkDwAQEJVSy4MFnURapcRJM9xA4N1Lq/h+ePLVyUqMPYb639l wBVBv3c+XyVI52MtLu0aQU39J8xPqQri9WHnK9uGAraN3lXTFCTz5qhjKyc/ o1NPPN5ybRPEet/cPtlMH1lrf5TswP7EfsfOPlQhn1X0eR/GlOW1dS3o9UXL vluHsD97/TvRJmgYNyu831iQVAKgad+LOjiP+52S3CmGjz+CuwX+PaC5u+8M 1pP8b1ngIHJ999eCc1GQrp/93BKOwP2tF+95XhMkKynWUfO39WjngpqqsftM vsyj/C1o654DWiddBckeimi2JxvRplq+C2KvBElpej+1t+yFGjd/eye/w/nZ Xn+Ei+A6sVvp1wIEyTMU1XzhVzRa81ltePlX7M/R2JHbBVdpdywt+44x6a9m 0wiX/QswcIkVJKPo9fj8ZwqSv3KCtfUn1qtATp0bRbJ888J7UgTJbVwg+PXV 73Chb06NX7YgeQgALr/2fDhv40ORw38FSUuKume4OBmJ52/bylOG9VLykNOB RM6NWP2oESSVAdvnTEYRFJwNe3OhWZCsoKizySNliNf7XObiLkHSH4Aqm90/ IFCVH80dYPjH+1VT4Ex62fL74wzfS++XfWjC9MUR9TncP4tdYYJDcGRE50ET rxBtZ3El6rWgAVcQ6SUihPOJWYfXwZ4ViXV75wnR+VhxSSKFqANdE5uUwf5E e59lE2oxXANDFYRwf7ZSRC9s6Gm6eGoV9qe+rNxah2oe+byTUBUiOXMUpfvx K6qQM8xO2SBERtL3zyrTFFQaKzp+YyvD574vtg8V6mesXLUD5we1erUlMK/l nmGFjhDdT3PVTfETKNtx08NnBzGuV0w+N43SpfujoBHOz667Wt4LOWFfG/pO CuHfxzy12QGIdltIBFpif4XhE+tHUUKNzPaj1gwubDKfQbF2RZf5bHF+6nj5 h2YUKfrMJ95eiFwN2GdURAthWNDOHOt7jL7xqbJ+FAynJ5Y8YvqlJqZJ369K Y5QKngmRe7jAvvl94TDg8mVj9ktG30eZzYPoA+/KxxpvMR9Iv2NdCd9+qI1p 8WP4PhkqNyMvzddNrz8z9kqN0XLokXdQSjeMqcfsiW8zdDsrQE5HC5FZo1T9 rgwWejaTbPM9kel325nmXujsddvXnCNEHgFAYt9iDnRSWZ8nlcXwvWMdqYP3 0zun0vKFyG4qmSyO6UIOph9X25cy9p9adRXQfsTkuHI1trOejPa2oeuu859U NTJ825pKsqHNirwfrh1C5EmKvuCRv9BF9Khle78QuQAAndKpFnjeUHv+4Cju N+dao/gwtOwZ3fFpBmPFlccDRqHZo3BbIx5h8ii9P9x1z4Umchf8BYQZ3LBB NhsaxyoUJEoK0/kp0cfGDeiIfsXMpUXC5BrALit+WwcPtnislZdn8ER4XSXM W9tSarpCmKnn1ctGpHdj832fNcK0Hk7MgyvtMCfpmVKVOsPXa/WqDe3jriuU 2SxMPw9i5RrhGZSpu97hmLYwWUZRi+6vKUZ7Xj5a/noXg10NVUpQekV5Xqku 9q//8ExkDO1UXGs/30CYNKSfD1dALuRcuK9wxJjJ79gl04OIiKJsD1NhXD+5 IGYC/h5bcf2vJdZDxhCtTRBuv71E3JrR12TY0gqTHuem618VJoMBkDu4JB5q 5cvbPL+J+QiK7duG4qSvL8q5i/3Baq/TTXCjaQZH0EmYpB//tVCJcRT7Seai jgvuB5BwTC6GGt2X5ju7M9juy68KGKmRjNK9MB/r+6JlzWidw7zzPD5M/3qm EqthWMo5iZ2BwuQxiuK5qPADrRVKTGB/FSaNKco8ZdUPFGIgapn8neFrvBNb CZXfmovMxTD9GTh5oB59qY+OhUnC5FrA3lUQWQJXKvGb3eUwuHIivB4G2ZwQ SMrE+tnsl8Z9cFlcWOREnjAZOkfx+H4OQQGz1InNJcKkEQCL+o5kQYU9R3ns K2lMz1sOp6OQXOmk0XArg08o2/5A75ccoNb3CJP/KJZ6w6katPhMQLDtEJOP Vy+gFL4NGT4cMUHrB8CtA2bBhUN7p3vnmPzqhwraoNeW90EqfCJ4PZzw0WhH 8x/0HrgkIkJ2UcnpzhtakGc2Of5NSgTHD2xdlwslJb0COhYxWOfFmlzofqxd V0ke+7OW62xqRGL+W4fPrRDB+fN9Xv6Drm1uH4LWiNDPJ9lJ/MMUEl7XuKdZ HeN62Udyw8jlpmb/0s0ipAkXCCixCIL8v568tdAWwfXs/HmzFj3ird7hv4vh 22XjUgZ59Nd11+oyeM075xLo9OqBl5yBCHkMgP7HQrkQVJdqnzTG/ObXdysM oPvLlNvfmYqQCwFH3ZXTBGes73pUWDL1dZtxupFDVMGWRdZM/OaKqRw4ObG0 2eiqCKkC2N+975bB2+RNV6+b2J/yUtjVg8aeZG8suYv5wNPRn61weOFVFwMX jMl3CkldcODzgup8L4zZY7pandCm1+qRqI8IKQLIBxEnh2CvJlLVC2Tsozfi 2uBlR4nyp1+ZeLOnP+h5L82Snf1dhAymKMcnqmlI4WXFRfdYRu/0QF4bMjQ7 aGT4E2Mil32wGT1dm07IpjL6VkkatKLfE1vWNGQz9VZahDfB4YwI6S9/RchD FPXw1rvfSPnVSupSmQh5a4oy91V7jE5Z+HSur2X4rA8YtyFPVanS8WaGr6im vBllTTn//tWF+wE+rjpQC2eyZoIfDoqQpRRlM/6jGq33vv5Kd0KELKGonIWJ hei8Zcc9CYrh+yNb14t81Mys/vGJkicAiDr+IBsWzpQc8REVpfvBPnLm0DTk z9HVPj1flPxK75/LnueibW+SlZRkRennR2mpXB9Ftmc3zutVFCW/UNRpvzd/ 0Jf1oTPRSqK4/4EuMo2wek6x/fY6zEfGOuaOQsm810XbN4qSsfR91SA0Ae55 J4p4IWPX69Udhg7nnb7k7BQlTQB4qKqbDSM2THh46IqSiwCZ+VOyB7YAm7vG BqJkJ5X8vsS2BS0uaD4nd0yU5AeKJy7s4tM+6HPCoOkUEy++Sb0APrT6uzX4 LI5np90T7oIJG/estLkkSupRlJ5LQjzq5f4poXkd57eojeAZgssK1acmb4vS /WIZWoxUo2O+X1qSWTiew72Dtxu6XpT7+9gZ56fSD95rQymbPRP13ERJVcBu 2sVdCcd4BYOkvBh9IVfYTWht8T338veM/jnuuRZo4T982zdQlIyj5/WA5mTo fdn6zJlg3E9zIfedYyhnS/2B1REMv1Gocyui+I20+n+IkifpeWtB/V+oWZqz 7Adi/Ne3PhpB1oGk2N00UbKYYq2IWViE/GzixskcJl6l07UNlWxTaeIvwvnB QpdrzVBQ6GNeXjn2p/QlFEuQdtmieM86XD/HUvPWGLz+yS3weCvDb/fq6QAK tuVxle8RJdcBdpFXWSms1b5j3zLE1Ldzz+tuNE+k3yJkUpQUBeyXC+zG4b6K s3q2QIyp/8y7RnTvc9XGTQJi2G7hrDEEo68bKM6IYcxx/R01AtuJTOFUaTGa H3RXpdHzkhgcfbJEjByh6msLDw2gw1VR9QeWYT5Wm3pgO3L+qpQzf7UY1u/9 YE8R+mnnG1upJkaeAiCFY5MCB3bM9/ffxNjX/9YrRyslnj49py1GqgHQsiyq HprUzN1Yu5vBh3nCa+GLb3Zmg/sxP3HPLaQZpdt37Ys/LEZ+oqjNdpEFaHKX xYZ7x5l6qsJUu9A6qbL/dpmL4fU0nGbQBNvc2py8z4mRP+n7fqNJIvQVHm9v v4TrC0id5B6Ahk8EDmy9LkYWUSzuru0lSJRXJtr1NuajbGrT21E6W3lR/X2s h/3jxtpCeHdWy3H9Y8wPHhweaIIaDrqND5/jfihsfm4ygrrGTuwteylGIgAc eVUS4ccbF0OV34qRZgCYnwYceGLAQfKuH/YnOr4eGUaSV57fzA8SIz/i/2+t yUDZnT5VCqFi5C6K+sz74CdinQ8jrkcx9q4Vxhy0qRkFpceLkR0U6+5gUgPq M88XWvSb8Q8s4P6JPtfU2linM/176DBSCk1P9JX8zBEjZQDw+2fYCqXL5rTE ixi87YpaF8w9IuFnUc74xwlKV0Knvwo8MbVipDoAuZv/VMCt+upWfC1iZCBF uavz/EGD2WT+sS4m/w/NtjYUvOewRsiAGJkMQOT8T8nQIvX0m5kxxt7NF9WI ZIjrMwdnxchCiuVeE1aH/v50Oh3II07bqYCy6VbkrPUqc1hInAygKMWZRxy0 /centXslxen+mAcd/TSJxtbHerxdKE5aAFDHOZQJv4enj3bJYTtrAaLn47Nr /5loLxen6+EcVtDth3LBrckvVotj/SwbnWJYumJsRZOaOMmh97ObQzHweSD/ M81NOJ6odH1F37/kF/U7Q4bfbSI/D069VzKs3In5yP0LxDth9CKtxLW6mI/d cKKoHlp77ZO/fwjH+985ZTaEFKVOPCw0EienKGrKRYbrV4WbdccyU1wfUeAq 0Ig8hB0O3LQUJ08DMKminwF1njyLzrISp/tB/UgKKkFzPD6LZK9izJp+1l+C 4tihjpdv4vxge7FlK7wy+7Px911x8hEXCPIpC4UrHPL2SjkxdlMumVZYM1YT esZFHK/nE/pbJuCrG72Sce5MfU0XFs+i/QOzNwW9xcnHXED6juNHyH1FvNrE R5z0p6hL7LG/KLFTnvweKE6uB2BHH31/sz2v9pn6ytTnr9UyipSbCeEj4Ux/ q1Z69sN6c4OrQbE4XwOv+dgMfF1jUTqWxNR7PESrDR08cW2LbgoT/0JIbRjx lz3w88li/Ffv3D4Efx3x5OnLFyctAQiyNU2Bdn8/WpGlOD977vyZeqiiH5Pv WSVOttP7d+yNVtSSnabR2oAxa/l/i9uRz57SN5vbMR/n6q+AAXgktWXmaS+2 J8/va25HwsTo6ZphcXIbRU2G70fo9g5lwbgpcXIxILl8C9tg266T4S+4JGh9 lHxCyCQy3OtuaC0oge37HtLnR+q+lKmdEhI0v2LfVrVpqK43EiC3ENvBZmut Xuh3QElnTI7xFzL17IaiBia9f5djf1CuFDcHHY64vfq2RoLUAOD2I9c62GHI 2fJwPbZbhMkaDEHjY8P1ploSWG9o+eM2lH5ilfMmAuup1xxaMIA0TE+oSO6V IAsollPzp3IUYOZa3KmP/SnrufFuJH46+XbaUQlyC0WdOzGAkOOZIXlfEwny A0WttpDMQN3nVmbYn2bib+4vLUUmVscvGVjheJaqhmQryr74XGrNVcb/8VxF Ktp05Xc8jz1T347YT00w6OrgqVpHCfLtZopamqGB5l1fwRv/kPEPfB2Yjth2 x0I8nkmQL7mAcqFMKOyzf2Zw8aUEOUyZfyaShpHpnV9ju94y/VG4ca4L5twd +PCfP9ZDTWs8qEZa95fvGv8sQd8HDMyM93Jpf2EbdxaG4Xhi9ITzDJJ++PRF SIwEKQY4IOD8IHR6jDY+SpIgfWg5m89koYEn/dWnUrBdcdKTHIFmz5Y5bc5m 4m/cODKI8lyNlKX+SpD5FNXR7l2Btr5wKej6x/TPHQz2ouCXP+3SayTo36ua SVoG16+FXn2yfs0S5AbATs15XAYfvV6acquL6dd7pTO9aOit4YXDg7geTlXu WD+08HkitnYC24nHO9RaUIFvUgwv9X971JpmKF84ptLPLYn7GRjE2wWNDksC U35J/LzXWQX2Idfi1SXZQpK03vrvScsnUdrRXV82ikni7+HYvNVlaKrU9M5H SUn8/VmL+6tGtN7YXl9CGvsT2fkfhpFV+QsFx0WSpCxg1xgH9EP/49+GOmSx P+v1D74eVFaZmmEkz/DdfHysDImdrHmbupTx91Rf1wZ314xeUlspifcrpfFT PL/unpIgPihLkhoUtWF/P0LRdcrzhFQk8fdxZlUSGajTfGfrTTVJ+nk1zGfx AW3FxpMJTRpYj3+3QPYQOmZ58/mhTZLkBQDoyTgNuje7m6EtWA+lvKamGWWc DV6/WhvHe2y9TgHtmdYU3tekJJlHsY49MShCGy5Ul3Pvxnyss8rtY+hix0jI VR1J/HyHCveMwUBr8fs1+5l+Xdt4gEIVXUqHdQ8y8dr97H9I8vKOFXGHMX9k hdleQW2dXpPxZUY4nm0anzgL/aQflrCOY3+q2d67GI1sC42oOYn7QbbLjrfC /WdKnm8xx/7kjdsfKBjwbPrCa0tJ8i1FhTdJp6KxqOW7h88x/hG+sAceqNRT NLBm+E7K8FSiIGA3E3ZZktQEQNCLXQunlD5UCNni+onw+nu9yOBQeuz5Gww2 FoJN6It9j0eaPebjuOY9boMzvtJXFB2Yen4k2RahoxlQ99495nnyPhnrQyE9 Z1dWsSVJawA6tFUzIJB249r8iOlPkWfmMDTe9qP21ROMG1TvK43CMMvaxIFn jD9HZ1ce5H7G9/qAO/O8qkLLRtHxKNXrIS8l8fd/MtzlpSi8wuiggDdTX4ah cRfkA/fXnH2L+SxOL8gbgKZKX/hTfCTx94ibuGNrYPTBgqb//CXx94WlAR5/ kKD92G+Hj9jOLjL5WQPNfOV9yj8zz1Nou+0oik3fe0vzmyT+/tCpRDgeCvfY HH0ZxuTf5J9Ygizmv1Hri5AkWylW2qRsD4rfmiyiF4Mx1bOssg2JW7a3f41j sNWBRf3o7FOJdN4kSVIAgCMfhfm1kyI3B5z+JUn+o+erGct4KFlh7vibI0l6 0+PQap00dJ56cnxJuiQ5SbH6ZnZx/UKrIjVvZzF20TtauWjewQrJfzmYP9lP x7UBWd8EvesLmPX2S+vcDOJ8UP7jXsSsD4fobaNwYbrB5+5SbDe3sPw0hi53 336wr0KSzKFYR2qF/qHUeYGnPldLkpcAuOQ/nA5ltv7Zwl0vSW4C7L93Z0ug zenBBeZNWH/AxIpIbu10l8VDP1uZeC6V6Rq0JHJHgUynJBnBBYLFdofB6+XW ITd7mOcXNIJGUPbcS+fifkn8fWSmfkMOkl+VZKk2zOwPLPltE8juQNN21zHm +fHnrxyHOXbCSzonmfrSPa63IMUPGuN7ZnE+6pzd6Qpkn2ZS8hFI4f6Lt9i0 oPwupwiKRwp/r/mw5XM5XDEv9LmpgBTWq6nxmF/bYUvJhURhKXIJAJ/8jNth ocX0roXiUuQQZX4iY3gMrXJZrnhDSgp/v/hs5fcR6BihN/NXGtvrtfujBlBx 2Y0KFRnGv5NHahgpz/nEPl2C8xOyGg0NiLUy3aNNXoqsAsB5mVgMLNPvubxr GeZTfPBLagaq2EnrBqzE/smCEe+7kJMPXDmrjDElW3m8DVWknuUyUcH6OPaz Hc30vFEle0+NsUvx32lDAimHNAM0cH6FLY96J5E8mXEgbSPmtzjnsHQWbkre eqFNSwp/n2kjt70CHdweyRaCTH8KJLm60blfK9+rENi/Ya29+wB0hD4xh3Yy 8al2p4ah10/J/Ot7MD9x27VkEIVtdW7z3sfgXDfeQZSWOE0l6Enh7w858t3d qErr2uKagxgn71ua34CG4ts0qMM4P8W7z6wMCW021V9mJEUup6hdG58mIMW4 onN7jmM+FvDeMoS0NuqwrE5KkXIANJes6YCHYtHb52bYnvz7jc8UOr9BIzr8 tBS9/g+567eBX/ejv+YWncV6OV/POU1B7/X/tY5cwPEcMvtjBwyL9JxbdInR e8bXfwqlqwnKbLNh+CdSzRpgdfi99WbXpMhlFPUcyMaiIdXh/Q/spMhsivXx cU4tEv5udTbolhT+3jPT7loZXKZSdy/LQYp8SVEhSz+n/o+k647L6f/it71p 7/E0RKTMJJ9HV0JIJVJIpYysUkQUPZKiJZEWFeorZJRofR5NTQ1JW3vvvev+ +nx+f57XOed93uecz73Pva/XPeeB2z8cCe27g/TEvwu9NcBkbdEXgXuIDyF9 nGcU2L/bWbzBC9tX6dELIGNNcvsRH1xvxWPn50DoW7XFG76IX3TLe55p+Ek1 WjwiAOMVGInVgPw40Q3MIKzP/Ng/DZtUfPe3PMX1EP5sOQEn31C2bKE436Wo jhbAr+zirhqBzvcX3rc0TrrK676Q/S+RntQIX/59BYo2ny/H4Pxtnv/oBkdi /hY+foP4xCzu15gGFxUOtiX9h2VbA+Yi8IzKmv/7TojcuUT5qdz8D0bIaYnN JgiRMzOU7qZTnjDxxQcN2S9C5GOK0mz+mAMLZRQNdL/i87Ny9/ZR0BLx/LTt dxSPoXo/aADMSPG7PUhD/Kn+TPsRuDL83rN4iPuzI7tuEqpKTn8sycTX22H6 5DzYGXq5YCgHn6dwn+XnxWPibS1C+UjWHfFdvp9eCTGf21KEryfH7baLwEu0 VMTiF66XQaHREnzxVG+9Wzm293zq0QWThVP3RlVi/O4tK8dAyZP1Ntl/kd6j Lmz3AGwTfHOroxbb90Wu6oVzjyWfcjWiegp6SEax0oVXBiasbcb5jFiJtwO1 QLb8Q234/E+/OdgFSYFbzVc7hUjn5fejM/tzgYX/0MzTHny/+F7FNQId+c4I p/Tj+PlqBUvA27duXf0Q7uftGrVpGMVjvGdxVAh9j/rYqHgAfHuYZ0WbRDIZ eNB+AETwV1YOzmN958LrAcAIat6bwSq8LDOufTrVA66ZdhFKnMJkAUUdHuOp g+dEB9Mf8giT2wnG/I8Nf8Dx6vHrw/zC5DWCyGytLgSGYXMaxwSFUb0u33xO Qd0TLL1QRBhdT9xbU2fAJlnuN8oSwsvX2+MTjxdYmSpNK075SmP/4ksJZUAi RkxiVE6YfD5KUXL5bpDXVva3uaIwqUMwOsNKqsCCsrLfDxWEx/AIZhkBw51q e1atEUbfq3oqPOSgt73dQPmtE0bf4wJTr3r498K2tDENYVJq+fnYUzURFq7b ee34JsyvP2P3LEwf1F+ftRXZU470qn/w4+eD3arbEX6L2kupCRDjZPoqAAij 729Lv4fOwuDNx09O6CI+BK26oRE8mLQWO7kb6aN7T92eh64p58qz92L7pMRL I/DSrSuP1hwQRt8Ts/Gl90GrHdd3Pz6E8yFf5FcAk8Xbi5MmqN5Zf/5j9IPd mfdSLI8ie904oq0Tat176JRrjvPRM3n0D67Z/Xjd2pPC6Hvb6xaXR4EMx/PO ICsk07rZd4yBFQUvoqdPY/+Ml5dbIMujN8etzgqT4hT1Z83tH3DiwHuRn/bY f55nNQW6+BNL113G/mbfJ6dAXVmKT7Aj6o91dpkcwfwV9GPXrDOSNeNcn3Mx f5j+nLe+IUz+pCgPkVsVMFH017f8W8LkDoJRHJVdAWKrKx3X38H6e1/YamFo WJ3aMwbCzzLIOjQLfE+0tM/dFyY/sxEmGjKhwF22++VpH2FygCBsgxKTgGPT oHmhL+onLakNsNJtYyaENAORvKFN+ww7/ajtfEnIE4z/9OGbKrhPhdV74Zkw KUJRAsfefIM6XdykXRiuv9sjvhm4Pn7lXFGkMPoeWTz9Vj+kXRRP3hAtTA4S hPCkbCIQVpdzCH0tTMoT5MaZrE7AMaS8ZikO2XswP7/qh31OG1+UJCA86967 m0dgxeROwfCvGM/PUL0f5qbsKaa+I3/iHP/oAPh+y9DrXDriG7QqPJeTHr/j yM5SJtJnmTI/dIHIxeMzm7NRPZsZ6R/ZmYGZNkkReQifelj4axoy7p2/zFIo TAKCUR3I9Rtc2+2gal+C4/s6Oo7DcxwuLWVlwuTw8vtE4fg3IK1QVDP/G/eT sRA5Dsq05crX/BVG30fL5vkxgaepU75ZrTCZR3lUCL6vglqXfzI9G4TR98Wi bdW8zL4HUt8+NyH8ZlX20SkYFX0lobEV5ad75lFPHzRNy37D04n5bBhSrACc f8QitXpwPsE3fHtA+sCFYLt+YfR95fdFko/uwPnjUdAQti/um1v+faMJ32OO ovhUv5hwLazefs61bwLF9/jYpszP9D2S7igxg8+H4dyWCbDzyorz+vNIJi6n j46BMW9bK6clnH/WA6EZGBfz3SyKRQR9v77eX60XWqTzHiphF0H91uGUHIP8 VVb6M1wiy/4xPOlnRkDWYNKOVXwiiG/0uF47uM7Ftdl0BdZf3B41DtYonlzr IYT8qfuccYuwUeezYoIowvfwCTAZhEFH2aTqJLC92K2js0DfwVyQU0aEzKU8 pmUzquGMzweuzfIIn7AdjewHCa+oJWtFEbKMjWhR/hQMbDKOTPmrID1ZMBLY BkT/vh1MW43iZf4umF9+Xh2a7+haK0LeJgivLK584M5t0iiigeLZdKXQR8EG pdg/5EYR9D01q6DfMOzYMVN8ZYsIOUEQQTeupYAwM8OciG1In7kgKDkADR1j 0gp0EL5HmkH5DCQeTXyZoIuQCkTW2aETbSD5tUG84i4kE3kOR9uAPXwRbaQv Qj6gKJ99hWVQtnrkuds+nJ/DKqe/sGJYPzD+AOKTlX/DZhJ48YQ/+HtIBH1P 7mD/hwm0lQfdWQ+LLPeftmXen50+AHZd1zyK7Gnm38UXQMyxkEuW5jjeyYH/ WsHRq722j04gmdF+iTYMuH3pJ76fQjL5ol9qAMA3Tw632+B4j749osBVZqeB 4Blsv7Wffxio1Gwn6edFyByKUl43XgFrRwK2XbyI8vdIEmP0QX/eNo3QKyLk ToLxq2qsBpAqWqp5VzH+717nQTBB95UbvYbrs6Nk/zyMN28Slb+JZIVHfAIz 0NJpE//B21i+e9BkBgr6ebO53kH52SjrVLPQ82Lr52IZIuj7561b1KaA6w+N sd/3RciZ5fe3XdZJQL3Ws3fJG9f73vk9XaBltLplnS+yzyq7pjAGnvGtq7UI wPUIO6fdCwxWeZQ/CBIh7y8/z53RLoALO//kJz1F8YLe1fGy0L9YrP7R/FyE 7GQjHha/eAbsnN2+8UfgekeG72Ola21q+qb2EuGTDh0e44B3jPy+NwbzmwgZ WQL/Et98t3uDz0ewE7MPfnHiTGH8J0JmUx4X5VIb4P2NF1JevkN66tGHuRZ4 bLQkJT0B450/+XUJqCVqpNZ8RnJMFX/sOFi4+iR1IgnjX/9RNQGeO77NaCwR IXUJRtHqC79Bu8MmpkmtCHmXIK7e6SkEGxyYP/I6RND37y/fL/0CbBq0zNZu 5E9UeAfNg+pBz8ylPsSHIuXnK+G7j52ZMkMi6Ptx5T/t/cD9ikGW9ijWhz91 qYHG6z9kmU0gPSEf/l8/UBoUyHaeFkHfv19id+2CUwlXsx/PofoQ4eYnWOhF l/9kJywu94dqfmi8noX5Ql0rp4gQRf7mKgkd4OpAWE4Xmyh5j6IM2ovK4e6E +Rw2LqRnsPY5dAPxy1a5NF5R9D18XF3NEuxdl51LFxBF3+/3WttVA9ivnHdC UBT160teBxf98QfvvJsiosvxMp+2tXEybS/15j0TR/7NdSJm83DrOsOfiVLI nvxT9pGVzt3/6WeZrCiqr46x4QJofC+U36+A/FdWeOwimJ8vXs/nVkZ6ojvx ygjwXFuTv0oV21vZyVPgWN/2Aj01UZS/bfXpLqj2/kWBtTrS0+jLzzRg4QJV 4K6J+d5oyv4DytVsC8M3iZJLi5RfQ/0b+Lo3r/D7VsTP+uqqoQV4493qoj/a oiQbK1Hx4HAM2H/Bt2hkB67H6dtdw0BWbbBIQBfxjzkx/YSFPtJjXLxWD9dz H/muF+TGJxXv2yOK5gHmU/tq4HN7sZIzBghfYWiBZxReWONacu8g1r/TOFsL QU99SZQRrs+KiPgluDKe/ivjsCiaBwg7RWsCbedjftUeFSU9KCopdXsx/Laa rXTSHOe367baGHjYfbZU+CT231e1avn6fVtYqmmF+S6liQ0CzfPrygxP4/r5 BM4vgKYLCo4fz6B6UQkq8V3Q/7KI4Ap7zE/qa/sE1HHkSnS4hOpvPfruOMHs dZo/XO6A+Hp8rOSrhWHXh8c0nUXJ6UWq4Zvpa7j3ZvvTIBdkr2Agk8jFnLhV s2XUVZT0JIicPU6/wBv3kr+H3XG/eB/uXACmHpk3kjxEyWbKA25UaoGE51cJ kfvI33jJ0oST+cnrbeo1b5Q/413IzlpwyifyeNUjUfIORU3VU0WQ3/fx3JYA zHfPC+N5mO5/PzIkCJ/PVhA9Cu0f3wRTT0XR/IC6vtIQkAi+9O9YKJKJAla2 FpD/zPpuSgSOv7BTth1eDz2iIBmF/Cm7rJejUCliX5brK9TfkcvGRWz03y92 nK6LxfYv2G53QUa0JqtOPOazJHo2D2q8Vn4T8UEUzUtornCqhY2xEvrzn5BM nQ7+XAn93vJ1nkxC+JkXH7iNQJ331AP4DeuLwtA+hIRxVbk0hK+bFrC1Az7/ 3F1wByI5M7C8agDuSWqwb8pE/LN2DfO1g4nkch7dXFHSiyCOJSeVgtcpue+j 80XRvEPFt3NjwCQ95SBRjOzJHWs/tQAKfhiwKRUl3Slq0SqvAH7KjA7IrsB4 Of85tgPLnKcaSlWipMMw1exYehPy/vQp96zB+RY3lnXBtAK3q+31CJ/GMco9 DuyLHYX0m1C/PGgWuRxM8VK7pNhWUZKdqP17qViInldufoSjE+nL+2aCWZjX Kg9OnO0RRd/T2we7TEGlv7oh+f0IryX4V/o4qKjZrLV6GMeTjVcbgHfrV9f4 jGG9rJ/MGFj/T8a1Z1KUZFIe1uYVTbCxeaXU/lmEpxD7/f4M9G1jS3+3gPtb Y1LXA7Q7p0/wEmJoPqT3/gqC3t3dP3+RTQzxzz8nMAKe9zW/KOEUQ/MUfdtZ p6D+4B+6Oq8YuZtgtISkNoCx4YImfwEx1I/8Kb1u+Gosw2NQEPm3+LQbzQCT yc80I1EkE7/0dJfA0vSb7E8SYmTZPHX+hsQzmDAXartSRoy8TVFWU1QZPLno x3ZVXgzNMxzQbR6EvAQjtkIR8SPbrRkEPZX1+p6Nq8TQ/EUiaOsH5zjsu56s ESN9CKKsn68EiHFb+oytQ3rCIP1NC8jjNVlzRBP5b9gg38pNdxbQL/q6Cckt 2YfCOeg0Qe2LoloonscTvvQhWC6szueyHeXbfPm/y7Nw55UrvZFADN2fG6R8 2JifCj4V5OgieTiopYaDKa80Eterh/mcszvVDwLdN3oJ7kV41LGUzmG4VO1s u20/lut+r2mFVzYmk1aGqB6MBJ4DS6DRb1L+gTHiQ1u98ygL3bBLa/GDqRg5 ukQFcD9JgZB0bag0w/F2Gh9iY6pHpqXNWuB4fvE+feDF5FwozRLxtQ5P/TcF +UzAjX3WuN730xjz4Pb7O0cdbJEc80Hdehb0sWduCjkrRuoTxA73qWpwwpoQ gvYIjzGkrN0BitN2DbddwnI392QX0BG9X8rjiPuxVthoAL53yPuwwRnF093y 3GAeShdx+Jq7IFkhRPniPHykvM/+rqsYCSmP8lyN5efdOw/3xrkhvKz99+P6 gH1tkcqvu2LkTYpyt7yRD2s38bGN38PxnI0U2oFBgGGr1AMxcprS3DjOzc9M 7Q7IJB+KkSqsxPWAJ+/Aar3yl+f9xMg9y/enhQ+N4PkLQffAQDGShxBcStVn p3NOHz7x7Qmut6fWhi544/BT7cZnWJ43udYOuz5UibOF4XrMFamMgmOc4pNq kViv4TPbA3/amP8xiUL5ZJabyE/CLRlhiTdfIT66rMPRrMxYsfrHUbHIP+vi s6hpIHpVxuHnW2QfzTLrOQa9ii0NB96LkRnL73tSwZVwQiVqrcgn5J/ZxdPO zrTzaObWSUT+5DbrsClQWUfrtknG+Nyh7CxMvS22P31SxEhlgrz08H0PSAp8 8+ZTOpKztB3OLz+/9Hbc+8sUQ/M77l8dCmDwblWbhSwxND/DWSDfBlmizu9U zkOy7tnW073w6ky87IECzG/H3cpp2GLaN3e1GNWPIVSpWQlMPq6rCy1F+Iz/ yqr6QBbXlZQfFYi/x5awxiro4eS84cQ/MTJ9+XnzymQl3Nlw891krxjpQlFa D2TL4KetaT6yg6j+MXJOAgJ0uaC5s7tHxMjrFBV7amse9O/boX9xHOMfffx5 GCzo31F6MoXsbeTkGnjol6N/EKmz+HpwSRCdAY2zVFPTAq6X9dV8Dqbh0V1M DkIczTf0FsYT9IxPnpHqbOJo/uT4vPE45DQ0kw7lRHL0nobEGXi4d3U4C6/4 cjyi1K+2DbzwnpO4LCCO+KtdqP4Hu5VLn1cLipP+BMG+Uf8n2JQdLbZLVBzN E/VGSNeAO1bOzz5IIDzdTO3IeVg4ry8iLiOO5n8u/OzJhSLhEsEMeXFUX5cR Zhu00uoT7FdE8cjNJne7wbs/8LHZKmxvmS6WDSeuPl6RtUacFCZsjC64jQLd FbYBa9VRPuTvvOX3H98PW/hDNFE8BY5jBiPwrwGXH7UJ53Nj6/tJSOuq47mo JY7mm9x4OVmZl+4nPKzajuJTq/oaBuF3mgeXLl2cdF4+37F3cyDLj8Pe70hx NI/kXpZfAQ1PqnCI6qP4WZqXB5ZA6MzU/bv7EN+s11Jiw6AtpIi19wDiU5F0 7Bkbff3mF/eOGKF41irhsgTTtcKB+HFYnGykPPhUtLpg7pVdHmvMEB7t9Yr7 42AFn+hSsIU4mm/KPaU3BI7Hd7kvnkQy8S7qbiuI3ZM2f94a+VMfFfZ0w+E2 v9uVtgg/s2mbJxtTh2E1C85hvW/0r3b4QG6j69sLSE+ZScQSzIp0tmmhK4jf hsqZiwRdxqLaxf2qOGnYSGXeajwPz03GT3Rdw/5NkQ2dMDHY7drhm+Lkw3lK 4XT/U7igaTSWcRvzPyll1w33ldKcVO+KkwYEY9owqQEEXxwfDrqH8AWrjj8g 6P+48h3mvbD+6OE39WBNXNjg2Ye4f58m9k6Da3qXLlf44fzq1YqHwI9mer/O Y3EylaJ2q403QJ47ghfjghH/aBazzwTzqHR7z8rnqJ/Wgr7kOIxO+Xb+djg+ vyIXlGZg39GHXR0vED/doSfcPXDr2ImzxjE4vvGp842A8Xh9R9ob7P+dy4CC JeqEncpbcXIXK2HDnfseiBdXtga+x/zWb78+CU6fj7OZ/Yj7oZ+k0goS2F2b 7RJx/5/c+rIApl8dsCpLRvw05b9acDP1dOX+aafi8x67R2QMBjQOn3yTgfSP 7wenCzBrb+XUC2TifDdPHe4GyhIhx11z8Hk91qE9Ax2Sz9e2/UT4MWtA5yJI O6xjfqgI6Zvz3rgvQfZh/uqUX+KkEguhXi6RDoz9m48qVWD9a9usaRihlvTH /w+SM930lCZhZ76X6XQ15pOo6DUHN5wx/326XpzkIIKiPPYK0d1Y1pr8+idO OlAUZNcthl36fLWqreJkCkWd2VHzD5o8HLC+17F8vlmIjo1530B6SWl3QzfO X9FMYwyorPzsqNWP40+GUdMw0DRoOmgI199uxckhOBPi5NE/Ko7ml8bF9ncC 2zpTrr2T4mQDpWuTL9wNf8lueRwzg+XDrx06oZaNmMT8vDiaJ5Ngv1QBYt5M RZlRGN9s/VMK8nbXqH5hlVi2z5Td6tkJXdamfeLllFjm09I3FTQDWq5EaJ3l kSBD2ImK9Tlh4ECi249MfgnyKUFU1sT/BMkTlnulBSXQ/TX7eS4bXV57Z9l1 EYRHbfQ81A4fuikcKxdHeISPybpxMPaDaFKTlkD8o37OdQNL1razXnIS6Dw+ 3yPJzizYkzvYRMP4SVv4S8GmR7Eu21Ww/sbmvcvvu78eLD5djfA9WD9c74ec gucfDK3Fsrh3RQ+8esRAYL8GjidefmEG1D9XC3mzEcnkUEvGLNCv55Vb2oJk RuJYwBL4JDcQa6GN5KwKdpsRIHW6VP3rDgnyGUFMfQv6CbxiPyUL6Eqg/hvU uE3Coe7HwF5PAs3LnRd9WwEt1jnl5exB+WddUH3GTc9xMDWU24/4enhX6PEy 1ZM2V900RLLutYLjbMznk6KWlcYSaF7pi2fUGCC2T7WrH8H24d+42JmX3Gsu +RyTQPNhvy2Y07A6M3W89bgEmpdTbTetAiRbhBs4JYHm4SaOaZWD93vd2EJt kD3FrlwwCUV9Lf1G7SSWz+NIcoanIP1uKV3E8Dzujy1Dg4PeI6gQ+d9FCbJ6 idpcteIbND1KKLM4IH/d4w13JyEztPX9SSeMN1uovgDXNORs+n4d9YvR+eRA KwiWj00XdJUgv1HUrmdKjXDh9AO9S26433GqVwbhubhzxT/v4n6MshQNwYqe faY0TxSfMC3UYqXrqKvV336A8iezX+tSINaR1/bvQwmyaomSSO/4Dld+7e/V 9Md4Rs7aPfD21C8n38e4fkkinSzMju2fZjuCcT7Gk/e56EZ3Ht/TfY7rNcKq OgZTs67yRIRLkEbL99cjC8+gErvpk4kXEmg+rvQH2wD037dZyjgGy4xI6w44 5Sv66t0bzG+z0mE2+umyyTXsb3E9br/zm4e/hGq+WL3H9dAJ3T4BtcxStdM+ SpCqBBEwuaEHxISFZ4kk4nwC/C/OAN7G2wYOyRLkBYpq4JPJgVo33wk8TkF6 gsp1XwCnhWsrP6fj+I3rvYeh/0fOsAomim+T5LNzBT3VYOup0SyEz/hif7sd dLTbKQnnYfzfx++Mg5Uewd2bCnC+PYycSagjnZ1wpBjVxzp4PQsH89y3Yafr pdifL8StDwSbyG8LqcDXTx8XCxeT2W+48O2PBHl7uYBlvI9Bj7dbdnU1Po9d OncpIKr03nu6DvN7tfN+D9Rl1h6U/If0WXUP7o6AixZcQttbJNB8ouynueXn 2/Gt1cfbsf/XiqVFkB14JvJ2F/bfJ+zZAQfUntpE9kqQ81Q5//YsQabkz+xV cADXr83zbhvYbTPS1zgsgebvrn/V5aY7zMt/WRxDcpZNvgI/PeL5IRf5KRxf JYkaAz83uuvozkqQG1kIeH0xA4z8ek9ZLyB7ImCJ4qPL2tflMSgUnwpP9+iA Bmzcvq9YJdG832iDx/L7a5SWcQ6HJMKTuULOgKjtZ0XbuZFM9AYTc6C46mkd G78k6ThFKZS/eQynHHOiVFZKonlFeyWPGajIN2q3RxjLnQs/FqHhfwpq58Qk yfPL10vaVDl03WU05C2J8BiWRrvGQGyj+9e3Mli/aDeRC8tvfnAtlJdE/fHe dL8DzAnX03sVJdF8k0Ezg5Wu+ombjXcV5lffvmsSHN6/rXDtGkmydIlad645 E7p3nA04uE6SPEdRHn5D2TDe45npZQ1sf/qo5xz4I50rEbAR4RNSE159YOnb aOPHLSj/ZpYvS3zMtYdpr8u2If66kjuYk9BswOj8sI4kmu/cajbRDBk+d9QF d0qSJ5cdKm4GwgSlhNENuyTRPOSNkNkOWMOs/35YXxLNd668IvAbsB7ncXfe h/UdSzOdUGNi266nByTR/OPhgz4D4MTjc5zJh7Be8MJMD3ywNqSkygT7N+Su /AO+/MwNmjyC45//b/gvbLQZMxM3lyTPUpSUYlMp5F6gyWw7gfCIqRzuNrA5 1LjF/BTWcxQ3/IRWm+7Gudrg/IMT2OeBb2nCxXA7SbKenWhx2fIEfLdv0Ew/ h/txdNprBLSy8U7WX8D24nJ7FgB/tHb6/GVJMomirKf6/kBtnfMesldxvPPl vkPA7m+IPv0aqldmkvPcGAy8msdjdQPJVJ9h+gJM5xsvu3sLnweX1bcXYOd/ is+i3SXJFwTROKRZDAa8WmfZGDj/L6eut8Mx21fW9vdRv2MEKpVY6bPk6Z+/ vCXRfN5h15+TgFBQXLfRV5IsXKKmj3zIgJyLLUEhAZKkEUE03RD9CwQaYqZm g7Ds8FPkDxBNs7G0eobjPVRWzQHSobScnFCET7462MZNV3RpWb068v/5HR6q hGuOxAT4RUku/z5k3V95WJiusdFmfPiVJPly+ff2ES0HbF1JO340Dl8vGQJR vEww2PwjNR7X46fjcj/1SqJV5BIkyQEqk80FjsH976x9732WRPOh6rcEGoCJ j8JIZxK2d7HzbgHmZ5vNDnzH5+E6j/cQsNodnfEpDfuXrmZOwTOK1ooiTKz/ cuxBO7hEyfvczEL1oiZZ3fqg87+mgYZcSTQPm5E+VQVdM6JMyQJJctXy+bwx GAg9wq1SY4sxngT3zinofVNenqcM55/Y2ULQA8ya7l/5jWTiZLkNQX+2Oar3 dxXKT2FhrwI/M0LIylirFtf/p372FHg1LPctogHJpK5k9iKIL/0nTTVJonnV 2tV32+GnDy8Zdm3Yvv4HOQG+PTrVVdApSUYt1+8JezGA5+UM1XuRPsv47PL9 JXfPv8SgAcx/Uo5qhMXKLyUmhxFf3acTuvOwguXUnePjmH8aLWsc1jTLtjOn sH3hNpZ/sInZaKA0h/hSRvQYdmZH5ItP3ov4/JxLaGah99+yFO0npJbjEYXr dEfAmLnsbWN2KTR/ys6yawHObm1s/solheZ5jZ5OFQFC9MUeST4pMnuJknkt lgw5x05+cF8hheZjL4+69wGBChmhViGMx2W4cw6Ifmq4sUdMCs3f/sy+3wel /SMb30kie0ZPh1sHULx4Um+FLJZ3+Lt1gjUGMvHOCsifzAqjTwBN1QaBGiXM Z/Gp3jjUYo+8tkMVy0S23hgEbSfqotWQfRabCHMS7M6S1mVfj2RGdSecAwei 6mPtN6D4HnX+3l3QxD2Ct3Qz1jv4w3lgfuLE1Y3bMN96azgGrLSlq0N0MN/G cJ8heHki/JXVLixzHHo4DG99kbqy2gDFzxzwyBuDjMC6Sr+DSPaQ+ahPQe/L 4dojRjjeg6+PWmDAgeNRR02xHMHv2w2frZFiTzOTIvVYCNHShAxgaaX6tt0C 83n9dc0iUHm2+cAKS2wvWlLZCgeKyEFta5yvgsf8GEymDgXZ2eJ4rmEBk9B9 68nNgWel0O+d+OqrrHT9S/bVqfYYz39r2Tjgf+Vyq/0S5svWsXseVlV7yq5w xPVKZ30/DV7wB2VqO+P8/XtDR8AZvZe2di44Xrfm3DRUd33PEegqRdZQ1Lsn ki1w4mNKfKqbFJrX3bwjtxXA9ryD7XeRzNjME90CvKQqhwQ8sfy3+vYQMDRu fqL9QAqdv1XmF9mYIg8Gttg9xHKp3WZOZn36bE2AH8L3UM0Z7YKvRzjdUgOl yM8Udax7XRO8qCoq3/4E55sp8nIObrJUzBYIwXy8Lay64NwTjTPaYVju8PPs hTkFO7jsInF+2q8SJoDvosH7gCjMt1tgaxsw3XzsUOorHI+mPNwBpS/YjbTF ovrFBKzN4KK3RV19KhCPZMa03CYu+vuqO1raH3A+GfqxrcCZ16/O9hPi73Fk XoGFqUOGuQckYv++6WouOuuNOIXUZHx+Hapl5kHxh6ScthSkb3nY5EXQg1sz zwpkYPvNlTs46CckSrm1fyC8zGc6pfxMpUP1H2yzMf7OfeIszD7PbqOAPCk0 /xxjw/EPJKVOjKYUSKH50UvZFYvw9hBLSFsxzr8l+Wcb1FNZqS1QJkWmLlFu OsaZkPeEbMO238g+kxDwmYOVj9Xu2lah+ET55Wus9IifWooBNVKk5fLz5tzx bGg7vzsvpR7n2270YAis3Xj4fNs/XL9W2dOdYOycFa9AK45/xK91HKa/uPRx W4cUnu+NHZ+HnpWuJrbdmM/Ubb5heIDbe9y/D9fTVnQLN11o59PnKYMYb5NC QieovRazvW0E6WmH509z0mPefWzkn8D4asplE9C+Od1j2zTmP7WjZQJuECtU sp3D+MT7jk44c+DvT/9FKTQPHuqiXAizGG32KYQ0qvdoRjIr/eH3Yb42Nmk0 /5xoVTMNTAYWPvFzIT05+FqJhS6pxGu6jRfrN6tvXgIt5hKTpwWkl583qb0Z 2wSZ8QEqYf6CSE8ozK0YBVdzN+5IEUEyI7NlgQLaszubWsWlyeQl6sjjI2mQ 0DS8xy8tjZ6XiHd/OJmFZ46rbJOTRvPKFtXO3TAo4lzBaZo0+ZGirghp1MCb NzyvuStjPivWfuCmW5lGKYSqIjmLXxwS9D0a6SWJatJoPn1c0L4RqPNW3/yl juOHNO4YBSJdo8rdmtLk2+X7b9xgPpjLFqhg2YzjiXcRLbDtpZq7rBbOL/bs qwlQdGvPmm3bcT599N0z4IvZ6arDQBrNexf1Ss/CsI13GJd1pdF8OVuaTBPw EAhX99FD+kzr7TUL8Fxvcu2rPdJoftuLHtIODv2s8IIG0mTiEpXrp50Gt7wa 2FBzEOOXGQdOApk73P9GjaRJ20XKfGTuHWQ9rvKI3xTzU6FOdsLeLeTW1WbY v8Qh5wusELRs3WWB4lGnjC+OwtSBmwGWJ6VJ9+UDm5XnB6ILn26/aSVNJqD5 7Iha6B37ufPJaVQvhvDLRS66A6PkScIZJBMHHq3gpptZdtMLzmM+9/t2jgGg zdbXehHnV8d//w9QFlV4vnAF5UO83soxAHhHdPQknKTJH3PUsET7czhacmxo 43Vcn5PJ20dg7VvnCMObmD9vqmYXzLwfuPf8bWk0b93G4sbK/M/6/di9O0jW jRZby8oM3JEf9YKB46V91foHXCTaDqTcx/0ze+A4DyzHF6d+e2M8gT3/hqB+ udSbgUfSaH5TPDKcjb7uw1ZjrgCcr3zBh2oo7HN4XjEI8fEwkOKZhLO2V96C pzg/6kfYGGjZ+eiI+XPkbxN68CUrvUA6jnIKx/FuO1pOgk9TWR/8XyB+FHsj yc8MqWw0fxuN8URbmkeg+6cZtpzXGO/MTPYoOOMr+qUxDuG1XOlJZKUfPLfB cjoe8fW4+3GiA27SM+QWTsB872U95aRLy9snq39G/lmNx4tGAcvcfZt9STj+ 6MZLi6DnbzS/7Td8nr5POi/C8sSMVPdUafIvRX3Ued0BvwfUnAnNwPWe0Nek 4MsL44JJP5brx0LMaKqlAK89K5m/srH90pqaFnhJcd2F7jxpNJ/+0efyADBd 3CvGWoj9V3SsHoE6dbbZsiXYfkycvwMqfrt7ZVuZNPmBIFjPN+UB7icRUqa/ pZefZyt0L3wWoo9c/v7zchXme+BO8xioMah08qn5v2x2bxb8UBmSe12P85td /2YCxBG8xfCfNNoPsLqsphT6N666UdOC6kHIO27moF9L3aU01i5Nvqeor8r/ /sETz06V8Xfj/rjvC1lJl/3KK3OpD/eDPplGMJt/p5wvGkT6mLelN3jpr0fO JK8exfwLmae74JmVwizeE9KkOQvhfpM3A6hqZB7qmMZ6xbiGXthreDlCbx7r ZzbvSAEOvvmbKRYZ0oKF+EJd+go2vLvGOMUhg+b9z10v74PjBbTSDG4sr7Dn 74Tfu0qlpPlllvlE85lXsjFdOdzOua6UQfPpRmty56COypqv1cJIznR93ToF F/X+UlvEZcgEgliSoXJB1mlPw6dS2F/p4EoupidDM3xUVgbtLzDP5GsA+tGN ncY0GdSvlH6DFsD149GmT8oyaH7+5MKDKVDcqOXBvxrJDFPP7mngP99ecnEt wsvkcJdhYxpJP5EsWo/iezQ6mc1Boe07z67eiO0PiPKPgSrz/sQHW2TQfoGT 9t//gec3wpbat+F4o2TUELAI2XNQbwfy131+3HgByiSPhcbsxP6R6sJToKky umNplwz5kSCuPn1ZAGJGDTee2oP8iW1O73uAreDcnQwDxEc3OSaWk6mi+bZY ylCGTGElDJ5wvwFdh45KuBpje+Hn473g3WWWM9WmuH57P8eOwgqLPxoZD3H9 jhj5j8IZ/bjZ6B8yZBXlEdzQPQTdM6Lv52Vj+Uu8QRckNkUI9ObJoPMU8dqM he4V/yxUoBDXS7z59hjgUnisuKlEBu0vcJKrboS+IY8+HCtD/hRbY0kHXMHv tdXtN47PclR8BAZ73s2MrpJB+xbu+jr3AvFZ1/15NVhPKt6chBGO1/701ON6 GLjWjgC5riunBJpk0D4BA4OYWhBjad+9sRXpiVMfpseByh9bp2MdMqQdC+F6 7DoE8ftPzd/uxnjxihdmoXqW+YPoPhm0b0CQdq4RftEyXZk3iPJhjHGf5KZv /mgY3jOC7VuOzk3C78r7lAUmcH9VMtZOQJ2IXR83TuP81zoGE/QfgmDbsTlU f+sNeQ/YmXo+Wtm3F2XQfP+NfzeHYP7ihoPRhCziV/FeZBbsv77uby6bLHmW hYjfteUH+NW3yrqHUxbtJ+B1DGelm5ym9fLzypLrCWLXMHsnqKqRvrZRQBbx TUxLqYAWRmKLZoKyqN/pazVZmI15K31uiyB8Rq7+6Ayw3sErFC0ui86TkVLm DGxLZI/MlcL+Xko//sBzayiVHlmEzzBQzBoGfVGzn/hpWH531LodOIhNaG9U liW3LFKatyVi4JjfUI6ZKsZrUNo4Al1Yew1vqyE5U/BR6zSccW2vjlJH8bN2 CA7NAffhfza5miifrNYqKw46ca62r3sTkomJV97sdK/Gyuv8Woi/gvOTw2xM 7iOlSxu2IzyPA4/+TEG/ooKHZgDnf5w20wJWkDnCt3URPsnzvmQMBH+HL6L0 sP4/b61+IL4+RTV3D9Zz/+sbBRFvEr90G8iifRHiq8V/Q3npBB1+Q1k03883 MjkBXwX9l7fBWJY0XH4+S96UDVW4XhmZmcqifjFufeyF8Xcia2+ZIb6MQw6A la4+EWIbZSGL5vHP3DCYBl8uBg3knJTF+w4Ew2bAllbfG91WWGZ51z0KUswf EPy2SCah3rZRoFPm4bvhLPa3aPSeAD/0b4ua2cui/RGHao43A72M61G3LqF4 NnVcfzjo+Rsd10Q5yKL9EebfTQvhgfgLSTlOWI4c/FsKS+XPgO7rsmQcRWUE JDRAkxCrfD5XnN9JX5kJWMV33GSDG+ajunLLJLDwPFJ/9C6qN3V/3Q8OZuPM oTO37smSaxep0C+hcdDG0WDopRfOX98gvQu2d+q55vhg/HI1rSqoF132eq0f ws802r00BmMsTpQGB2I5f95hElJCXdNzT3C+kQdp08CqxEnJLgTJWanBmouA 6bVoWBKG67l4OZqLLrvz0c3NL2TRvgkHL+0G4DYt+joyGvNPCX09A+u/xPxi e4Psab3mWlz07RfVpy/9h+M1c3tNwTDlVMWqd7Jov0XCxPFCMN242xB8xPqW W50UPPa8/EbsF1m0n+HN2YRh+M345Cv+5P/3S3T7DBDl6S65noL78elk4Si4 luM81ZiO7QXTTVphpdsSbc8PhEc1ioXPwI1bfQ9+zJYl9y+/b143+gWDhsRu iP2UJRtZiVTRzzFg+O2rmDuFsmQKQQQuxeUBo9PrSzpLkL9uwkwDBT9Kp00e KsfxnhltXgD8Vfq075W4XnzP9ebApYCKA/LVKN+WZ0P2rPTivZYu3nWoXx4N V8pZmWpET/RQI+aj/ezxInyYdq34WAvWh6uS3MxuZ2riR7sseZWFkIwfTgV7 1f0UVnfj+Cd/tC7CuE7xA4/7cPwtjz6OAPbo19enB2XJWIoK/sHfAO0sNKKt R1H+Hry/z/fDHKH0ooIJLBvq7e+DiiV7JjRnZNF+jqOGf1sBw+u3fNi8LOnE QphURqWAZvqp/QSF9ZEXhNvAzumea/ascmi/gVrOZhbmyy/Xoyo4kBx9U36A jblwgSjS5pEj0wjixuHUInBS2X88hl8Oxeu0vDYI0xsl5HkE5UhLguA5d+w3 kHr+xsBJRI5s6qE8nBXcoKux5rU6cTmU35tavgVYw53xcpc0xvcyuMvJ1MrZ W/hODumpX/sHKRjiVjkmpCiH9n84zu/uABNbrORuq2D7t6e6WZhHhnr3ta3G +iOS93pA0lsX5wPrkJ4KErfgZAqdZnmZpIHjOXfGTMGr0gEF0puQnJn38skE LP8jOea5Ffvbmc63A42AWNl+bTnSf4lynNqQAgP2bth3BMih+XkFWSOCPkBl OGXoypHpBBE7c/InOJi274XybjnyN0XVXfPtg++d/+T77cX4h8a2zkMedevR 8f1YH3zs0CC07+yTsTwkh/p57oX9NCiIurE3z0SO3ENRkx1kFlS1YHVSP4rs Pbzfj7bAB0KBkc/M5dD+kvqi45Wgo1gqf+EE4tNS1GjKQd/tFTdyxgrJhD/j BDf9NX2jTOlpObRvxAEoFYMcI97782dwP19rWLMx26zb+9TsUXyiZ3HnAmB1 gqYWlzCfFxZwASh7hqR7O+B6hRruXYL6Tx2Uvjkh2UN2rHAKnond59t+HefD pRnaC72+0caEXOXQfpDGEe0/MDZ/9jjphvUKua96YF5NZbbDXTm032PnmEUn 6Oj5oPbyHpZvvT0yCNjnvJ6UeGH/x3vs/kAVPqvZWR8cb+BGwzTUl912eo2f HNr/cLRDcQScWS9YdCwQy/q6CnPAa2fvhgdPEB4jcfP2QRBnnBP29RnWc0xK TYN8m0iiLVQO7QNJ+WI/C7ucrtsLRsqhfSjs70yrAef9QxU7o5CeEpm/MgZV n6lqX3klR65YpKynRD7BvXFUdGQswmOkpPNPgHPfa7mK32K+HfE1zdC7INFx 5j0+j9wGCyuY/9X61qh+QniZ5Nb5aZjfa6drloj5/F7FOgO65sDb+8lypDVB SLAt/QWc/OIrk1KQf7Nm8C425mq54Rst6TjeDa25BWCgUdi04occybdIOTYI vIL2uq/20rOxPqr/+gR4aHL706U8fF7SnGUGYPzpI+IRBbi+//SaB0Chs/rd wmI5Uo+i9siFZcGe+xxdU6XovNA81m0VoHOHNB1a9RvjVSaep8Ca/1K+HalC fBRe3BIgmAYpQXKeNbifXzbu6ID2hRcefKlH+eny7IyZhw/r9Aab/smhfSfP tqd3g3d9MmYCrUhmdA8lt4Di+Qm4owPXN2R9/Bjs4y9TudiN4+1d/3cO8Mq/ 9Q/rkyPnWAmbWZP3YK0mYyJ/UI78QRCSkh454AB53HJyBPMtj1Jlo188vClP eQLHe7whpBf42vKpm07LoX0mElJXO+D7ax1PGXNyaF8MWdhXBYu9mPOfFlE8 clu83ijoC3lu94+QR/tikmSIYsD71rGEj12eHF2+gbN/DgTrUg0263DJo/0m ManpFDAsUoy055VH9RCfUl7BvFw/xxoqgP1jb3woAv79fy7+FET2jDtFmxZB wkJC5biIPD4PQ918zF8C3jpKEvJov0wO64EGOCBv/dpEGssbwo42Q/4N2rwe cvJo/0pG6OcuqL5LyPkjTR7Va4fTiXFoaNpX16CM7a+ZX6+Bl+1yd/GuRnoP tozmCeh//cU77bXyaL9V/3kfYfrHBy5C59fLo/qvmtzaCwbAKc8HG7DsHRDW BtQn9MffbJZH+0tsi5a46Jc+qJ/J0cL8vzdrjID3tqJ/W7Yje2LCPKsT9Ekt 7KEAroeL6xMKqP1u/y5HyqN9Nd5ifL+B/cOS1WA35ss+zDcN43W/hp3Yi/U/ XUKaQM9UBM+t/Ti/zx9MW+DqT563Qw3lycvLBi011uDc2Yv934wRn5b7r15w 0v+TNbWsMkXxst4F9lGg68/20jEzpGd4DB7ioq/yU9wpdBzzEzaO6AFn9Hg+ a1ri+Af9743B2NkRBSNrZB+j0FLDRu/4Uht02Rb1IzP91kpWprJ9FovfWZxv 9PHgEWCrEO/8zh7jf6w8zUJ/Xf24veAS1iePTsyA1oCbR7scMJ6Ywh82Om2P 9U92Z1Tvq6lt30ToNgt7tZRd5En3JSr3iXMKjP6q8XaXK+KTOde4ZwbKKy09 vHsXy1277Sbgi6DSixleuH/0D4wZ2LjvW0OdjzyZQyy/QDzIBjLUC8MZX3m0 Dye8PrcbnPjuxRQPxPZ1PwfGYMSVyxpbn+D+Ge5WYqPXqxyNPvIM43uu912C Uo07BJ1D5cm+WSraWPs5tHiqfC8oQp4sp6i1asZtMOwA39inlxi/3lFkENSw jNuWxiCZUcd1YwCIp9X/6X+D5dBXtZ3g2NUcfd63OP8nZYEEPWT1+29r3uN6 vb9+note1fREdd9HfD6MthJjQPT5rdCzXzD+CJtdPzhy6DS311fMt++cEw89 mH3/rdff5dH/a+2flRZiVmZs6MtKw/4L5/aMA6FrkiebIeLr8TVceACarCV+ LWbKk4CifnJk5cOg1m4gmytPRlHUTHlEI6wIK/+ok4/Pi3eY7zhYaZIif7wI 5/tc62ELNOKKfnzzlzza91Oel/wbBP7wJp6XY36S86ANlLk4OCVXyqN9KY7F 5RQQWH+srfIvloPEWRaBYQf9yGgtjn928HIx9I9clbeyEenJ7Z/tZsAvU4Gt Gs3yaL+LGkc/Bfl4J+MM21C+tGplZR76gexG8UuduF5cxW7sdF/XPJ9HPUi2 kb1axUYv0kyYeduPzmdzYG8lC5O7++mF/CHMHwj0tkCDKLf6jlHMN9n3Vh/w MbM7yDaJ6zPToNwKXxs3Wp6dQXyydvE3LwC438yhYB7be/HH9IKa3WUeahTO h0HsGgVj9H1P/FgVSJclKuNESzLk1856PcihgPJxnFBaBKs3bU825lFA/nb/ VrcBPfWkn4n8Cii/gxLzk9BSdV2NiCCSM4dleefhTVpsj4uIAuLzaO+mNhgs LTdXI66ArjcX0aN8zATR53w60tie0kiZgQUrVsq9kEPxsg6WpI2CNu6HGks0 HL/s5/sxsMDKQtqoYNk2U2YJSCzeOpyzGvl76O8dH4ObpsdsVdYpoPPYXLfE Tj80eum6t4YCOk8JR70Emfb9HQ96NiJ9y5qqz2x0z85ToQe2KqB9RVcGbpfC l83V8QnaCE+3y27nDEytM05fARDf6N7k/1iYlX8KS67qoviEe9AbCgyW7vpX qYf5GvuKzgPuwvShLXsVyDME8VdYvAko52wmQvcroP1E57lUK+FOmCA0a4js GZqu50eBxfdVyidNEL7CzfynLMxrX6K2MI8gufnkfhmCGfheYq+COa7vo7Cf czA+Nsj83gmMn/LgYy3IjeK50H5KgXzMQjxM/pkGmsI8b+85jetz1ExgCswG z/u9PYPj++VwNkLRgOsveewxvsjJQg6mhs/gp0uXFNA+qIs+WR1g/71zWaUO OB+w8/AoOOPW/FvTGec7sS1nEdx1sWh/4oLrE1/6awGGO/6eGHdF/owpc4M2 kHzhAOcxdwW0D2Tg8lYOZrldrkSqB+6vX/OtRdh3CqhJ38f+nzu5Kchu8U3H 3Rvz/SbaswAUTDUMmx4poH0xe3wSWOg6hm9PkQGYv2xjTQU8upfm+DoI6W2u 35PjojuS4Qz2ZyhepjnLWnamr45w8LlQBbKIIPTTurNA3Ba/N4URSK9wgWtW gJmlwf5tbRTGz3LRXb4/rrmT7/8K86eVNA+DSaWpmqFYdF4yVQu7BZmCco69 JvH4fJ1S1RiDayV65pI+4HwC1tGn4B6h0/xinxG+tbaUqgDThq9e7maSAnmW IM7QnlaA2xxHNOu+Ib1ulfwkPzOEKiF3pKH4MYunclnoX2b1TV9CheXfCyJu 8J8EvXicaUdl4n4PGodOwM5BLZfTuQpoX9Ta94ZtkOj57J2bj/Htg9fWAem2 NWGrihXIS0vU9Mq9yXBr46t3PqVY9riqxYSCGvYznytwP7LUdTiYAx4a+2r/ 4PrNH59kpRf+ngghahTQ/iq92dpaGKuc0bGmHtlT28P6uZkMl3ubD//DfMaU ZsagZcE+z1stCuTm5ev/b2k30JZa8ftVO+bD3SrxD4heqlIo7sL6Kr4D/WAE RjiM9eJ6hQy4TcNfK04zpQdx/p+DnHjp8Tar+XePKJDnCKIsjfsv8EoaPHFp HOmzLKJMeOg27Mnvnk4pkCUEscWY9RcAx27PZMxi+2NWd+qAZDy5r2MB4/dH 7BqFc+5sB5efdZD+TpHL8vNF3DnnCBbacn0FhWi6QvTqsqJwDTYawp/KX89J z5tWz85hpyG++VouQyCJFtRzjBPpbUKqDFnpMfvHV/Zz0Uj7JepkyPVUGOh8 bJsHDw3tP/LaET8O3SPTrET4aGh/VcJvrVlwMU/W+y0/xnufua4HWAx6fNyx AtnrDgr7jcG94u1V5SsxP6F+479gi+7eBTsh2vJ5G6bo10SYSvbvlGeEkX1m Uu+VSSj4hP+gvyiOl9gYOAGX0hydaeLL/ksUW89CEhxoqwxPlqCh859g08PB rOPTyjaQQvxpi6u4+Oj5W8J7GqVxvlIfv/PSk08trHSSxfxqysLawWtv620c 8jS0H0un6mM9CPqcYxWuQEP7udzn+vrh3dpV3usVUX5Z+4J658Bllkcfs5Ww ffsNpTpwYu1AlZkKtk+M/zIEDY4YL/SuQvbkVKr3JNByT1K+u5qG9nXxd9nX QpU4sYPCath++NiNdihc5ur831psr9f2ZhQQ0w3hOuooH2rHwyWCOaSgm122 nkbqLRfwDOtd2GjwusdWE/WTkaB3VZhe7MQhOL0B5RfDy798XlIj7Lf5bUL1 onbUMybgf7klVgpbkJ4BpRx56M8GNLy/bkXxiIJdzAXgKRb8cd82HD/RSHYE XN05WdWgjeLrspmyEkyr8xYLjjpYz3KxfhYYBmUoswMa2ocVKxjQDXXS5A+G 0ZF9NDfzGidzTds9Z3VdGtq3paM63AfE+TrDs0ikV+j+/IyFyb7FIPuoHu63 /zNTQeaY5Yeent00tM+LFPxYA1serBC8swfXO7JofBqUfXLaJrQP2ZdbHrgk xIQ1VVZxBgjPAwp0szHfE9re2w/gfMCY4AIIU4v8WHqQRrpxEjYDVCSYGN8b d/8QjYxmIWK/9H8Bxj/GXmw3xuer/VHlEnz/MOrZsAnCaxbpPs7O5DxywD/O lEZmL1ApRq9fQ1u5qfsnj9LIDRTFx0wqgT+6X7kJHcPn8V9kzQyUTjp0rcAc 872usG8BuLjPXrxzHPPrExZgYVbsjbPdfBLXb/Nzr1mgLnT4RK8lxpNz7SyD DxsWDkdb4fPrMttEMDvi4veb2eD+10eWczPJq0d38dnSSC6ioqqlWYgeqUNs z7bD/TZSWMlFn2JP2HDzLJJbut3lCbppufma9edppNUS1R2rnw4/hbPR2u2X r9/l9+nc3jrAc+azRPhFhNfCeTBfkH5G4+RK48s0tI8s+0VzBcia4eTicED9 pd6mmw5B2dykpXRHfB5yTPZwMl0DrKauOuF+bxjfSjCrzHmHVK/hejxad2gW aip972y8jv0Nmy07oe/A6X/BNzA+tT67GXR9F/hr4IrvF0OcK6eA3r20X0u3 cH3kc9YvgaiDZ/OS3fD5kuQ43wrnxITgxTuI78j+snpBulkL/ErzwP22meCZ AV/e23+oZuDztTL+Aw+T30X0jb8nvn/ZfmvnotvrZkXoeeHzbyYyzkrP5bkc PPMA87/x+A4XU75KwveTD6730Y1DHMzbUbn3zjzC+dDimROw2t7xlrQfvp7u DkSNwE2bZZwq/LHecgNjHgYu5tt7B9LQfrVMUfog6C1wtgFBON8picl6oB8s bzH2hIb2bSRS9oLMGMti4/inNPLE8v10y9EvcEH1xj6rENx/df3NvEyLUUVd 0VCc3/dNqVMgOaNUqzgM10dzqHoWrPS+pcGIoJEly9dLgmgHvGiySlXrBY1c T1Grqy1zYb70b7mBlzTSiI1IFT7zH1DqdBd7HU1D+93CmgKLwZ3PawQsXiG+ hLVGayeovVXFvuIN5r86Tr4TbNFnLOTG4npOzNgTzKAV6hO3/sN8jIt+zYD+ 2pp+zXjUD5tVrdLi9L1v7rd3vsP32z20n2z011c0GyI/0ND/sdLn46fB0raG ysMfkZy14fs+Chxn9Snm+kxD+8SSA6SWYPKvTTnML7j+ey/c4WQKhjalXUvC /Ts8cZigXz7tm6iWTEP77B5fnWyCheu03jV/w/07bfJYgKky1RoTkoLxVnVS c9AjKyDsYBrSWw8827CS2fcv69lsOvavH99eD4/Njwe9hfj67Ox+ycnMllwd YPYD+WcqK18YhepaJx6xZaH6ehT2q3fB0CMBDxKzUb4m8QKOQnRWp6x71rmY n5yzDwf9SuD4HYGf+Ppw2/aYjVn7QfV2Rj6Ob9TauYK5u+j4jQuFuD4XXXL5 6Z+6/J0linG/t215SjCl2bMcfpag+B7nM44swQeK4xevlWJ+tj4MHubITtXz iuX4+uYs7+GiW1oetyuvwPUdOKBCgYJb/tZ3KpFMbJuZmgWbQjNPrquikQks yy8QERC8TB4zr/uL/VnVVrDSuStXHfWpwfW+zDBgY14ftjDZWof7E/0hewo0 8/sbttdjfnF/XDiYB9ZmGjxpxPebIs9r7PTv+8b0dZvQefYwebpRkKl4dtWu wWZcf2bMtRHo72lBj2xF9crSzpUQoU9H+23f347r467czcK0Zf7YOt2B7ZvC 58dgWf3oxrguGtqv51J7uB9un1HRONKD9FSi7rEFGCtmsZalD/eH9SnbOBTc 7Kf6uR/F1wzc7i/CdDP5oXRqEOcTJ+tIMLuujMrzDWP7SH+/SXjYT0UmbQTX 6xlt3xiA8eYS58dwfQWkxjmYa/J9RcQmEN+r+fLzwvSn7cyVuZM0cg1FNedw lsElYpTPaRrnv72vkIt+UV6FW2GWhvZzVZBJ3PS/O8zZS+doaN/f+X3KfyB5 3JdwW8D94G94NAc+3GAurFmioX12XzMOCzDFn43MVFPIvyUgwpyb7pmoPOnF ooj2/eXtWBiGg2XHRjexKS7nF23UuFaIaTHwaLCFXRHtrxp7eYSNnsfD7A3k RHKM1QTkpGuuHukE3Ioov08hhksgQl+5rY9HkawjiEaJuTzAYXusKYwP4T1W 9FIWYl71eFS/V0CRNFqi3m7+ngEbX8DqiRWK6P+RF2te18F96cOVrwURvo3k /BZOelKNUrmJsCLaf1S9ZqUQXX7SrGRJBMkMiapcYfoj4UcFCWKIv4cIBxiE E5ow94QE8mcQZic46NaHhjO5pRTJQ0vU16e+mbD4ohL8Lq1InhmjmkWXPOHW h2apZ2QV0T7DM6eP94CYuIfJwvK4Hud2s/RAvtyML1kKKF4Q0/OoGP1Gy1CC gyKux5+TpgS9bVHxnayyIto3FniInZ15SMYsrlhFEf0/9P9KuvJwqr4ufC4y dc2zxHWv6pekFDLswyFJFKWSVKYiTUJKiUhShDQZmkgqSZI0sU9ooFDIkEJu VFTm8RrvZ+/vz/Wstd+13rXX3uec57nPe61X/9cCkn/qFm+br4n0Co3inYrB z4eiTV0LNNH/NT/SSuoFS4PahkMXInzWA/l2RTKEgtJSizB+frQ3g3wvlrgo TQfHW96b0w7kaw9a6+lifNrBpAa4X1/j8XoJWl89t/6UNJntxQnZqIf6HVY3 bidD83SnEn8uw35tg7dypBWv4fFhfYyfU97JIBNKciuFDTF+drZWN2iKielI WoH4mN8PbBCk52/aJbDQGPkJn5wFXSBgrtncAhNNdF9QPosG4avfSkZ2QJO6 yOfvSc1qgeK5/Y7NJFqfOjYoL0w7Has4cMAc49vmLf4J0i3vnJ2mUH3miSox cnTP7LDb5y3x+tyUmy3QuN75FcsKzxcrbub7M/Lmsq+PV6F85kfmeffB6t3M IcvVGP9wnqwUrab3W7LOBsUTlx9+FCR9xosWetlqUs0E4dvKfQ3y36RYjdgh P1fDV1KQJOIOuZ1Zp4n0+hyutwyCtU7rgpUdsD2yXX0AJGssuHJ/vSbSVyx6 a/ET/uwkck0c/z//PeclyaV538orNmI+80FJJwg5nv9r+2YcL7mS5sIyq3ii xwn3i2H29h+QlfSZE+aM15celBEjXb9YGEq7oPr54kslpeistDkbbm3D/IVP +LbCkT3D+5btwPU6JSybTVour4p646qJ9PQ+qH/jwfjJzFub3JGf1bj+0Mz3 87sI+MsD79fMexSDnn9++5cjOzWpFoIYl7UoAwHOhgMiXvg8XPSvI8hXmtIS Kd4Ij/9te2I/FP/3Z4G2D+az+P2mXrA5/41l4R5cX/WBckE6LfTGjrX7MP5T iSwG3WUddLRlP1pvTrtcGoVG0hsu+friehvynATIyK/aOfyDaN6KY6OvKZLV 6UIfEvzR+tbhWB9BWm3/93bNQ5rUQYIwvfaqBvgYvJjOC0R4RUIpDn3wyfQF Fasj2C+d9vYLmC7bp18fpIn0Hmt3GNVA2wurHLyPof0Kv5UZwAOJLhp7R4OR TanteTIC2jhjkWdDML8fDbOnoG7351SVE3i95hadGhj8LLsgK0wT6U9ObPr3 E5SGRdWbnsT93GzQJErKrnHvq4zAfE/vjZSkXWVNZrtGYvwj/54PgKwmufm9 p/F+9G8UGYEjGd1U+Bk8jwK2t0VpC9+ybTLRmpTfzHzldzaBVDVPrcphTfR/ 3gXPFYaAyfJFup6jeF4D1V4LkXVrhlbweOg8uNlueCNL+7rTFvHjmki/bskb 9X4oGhRlpzWJ8MMUNZ0JOj3OYXPBFL5vGNw0YRpkKLut5yP84soSnT7QUPDD 5zfBRv93fuPYh5/QryYrIESAjfD4JiMz+915KERWiI3en/JkbiqQGdMgKnMW G+WvX2etRJspCCeYiaD4MN1nWcOwcVFVSp0oti/ow0EYYJl8e684wufneF3r gcytHg8JJhvpFy40PdUI7h7Ufp4owUb6iHlp6j8BFTVYrCPFpioZxE9Wy3Pw 7Tosfy2N/ITHvcZeEPjkdJ2zLBvpMW6r/zYMJMvtv/fIsZG+oOPDi39BJlep M1IB+8caV0wAy1Fuv6oSG/E/+3lm3pslsiZylVF9RaOcf9PwiNahWatV2ZQq ny8m+asKypgCqZY5yM/PY8VPwuwNs1QOzcV8uDdTJ6C1zye2mAYbnQ8r/w4J knsiSSeVhWzW2rybTDL4iruhARvlaxWU0Baj5bMXUhUcvN462WsK5rweWOMx D/s9z5kyaZuvhRtH56N+pprPE1Ck23ojd8T9h+vTkVMdgyHC9rs52pjfj+bM n0BxrpL/y0UoX5rxUQ9xMnc5N9hhMeIb3uD/eATY2t6P/KWL/NzysfOC5E/3 gPjjS5FN3TcpEyVPBJkmyyxjU3rT/CVJS3OhcrxQ+r3laH1x3NF9EyAv4+MD 0gDlC+8fetIB1hYmPq01RPVqjJfMEaF/17gV7THC/T0yZTgIwjv/+8A3ZuP/ ty5yFCFV+f2fr5gim3AmyqXIfIXC5kUkxv8YITAB7HUif5eYYfuDoP806LRc 17eFYlOdBMHVnSwHp7YqjndbsJGemNukszit7tcqGLkS1/NJ5tgP8CIqU0J1 FfK7mQVrC9CON/yVcq0xf8tYFR7oemKiaW3DpgIJIt+IVQeiygUXNa/B+TrP j4wA1o9K/QA73E8Op7wLFIxeMRNdh/PdMmwQojdJutnctMf52hdGdoMerf8c 9dfjfNX5HZL0WdP+beUb2EhfcllVSRtkOxZ4uW/EeGLL5/wA0OfUwZFNaD/N FcYoOdopbO2xWCd8nlo8FQZh3xWFU2xnHJ8P8rpBTPb32Bdb8X5vczPqh1pv 7iXab8P91JOZQ5CfdHgZzdtxP3Ns90uRRxNtnux1xf3/IHq8D7CJlBKeG/Jz 6+h4CbJiz5+qKA9UL99VlCtBB9Yaf5ffifyUqJ7eLFKdjOlK34VsVvVeAVHy /d1v40u9cXzINh0ROkB6kVjRbjbSi7x/Zv8fqBZ8XGndHjZlShD33Rq7wLv2 inlNe1G8eU+OkTjtu05Nf89+3B/hwx2CtPLz/ZajBzAfZpDOOHzNotefPojz W0+bzHwfxUi4yfnjeJf3gwStOLTjwK0AZIe5x3sy6KIdOceXBKL4tKEs35nv 4bLpaPowrqfrANEGZfUcku2CUH/DOv2SZGl4NfXu16P/78+WNgbpLdSXvzuY TQkRot4/t7NIaV/qzfBxzO+rvqkA/fJLQs2pUGQXWUzcF6U9LX60yoQh/LBk 4Z29kPlAryc1HOEV84OOznw/yEdMLo7AfCRudA1B9xOfxeEpdB8Sdw5LyJDi nWwV29P/76eWjgD5ZMOhBY1RmO8R11BRcnvhGwPvs3g/lZLjZ5HC8+SthqIx v3c1qQSZG7/LMeIcwvODp3mypAsv3106DtdrWhjKpIU8Zx28Gc9GeomMqfkT IKdic6hOAl6/6oWWBOlscPdcwQU20p+cVpMfgIzUkRSbS5jPwIb2bpglujqz 4TKbiuHzDb6AWrgpIOnZrkSUL8Gl6rIKOd3U8XYgiU15zRQgu/8GyFxlVBue gvY7nFq99BdwfHT2h+Q1nO+k3Q4RckL5a+/167g/9qd1Z5EZEQuntW+i/PzN EcQotO86xnyZiuqlNvTdGgK8zeWqq2/h+fyj58kk04tUF9an4/7lP01RJNcu 3LdiZwaeh9supgQ9fLFwVf8dhBcmblk3DG9Ozt4Udg/Px9aOZGHaxnu7p8R9 NtVDEAHs0xVgoCrb71oWtmFBcjG4bjx1YmE27ofw4fJRaH17Xdzzh7g+A4HM AdjLvHlt1SM2Fc3nG5sqNsLkIz33a3PZVBBB7Ll4qBlYcs1eeOTh/k9v5IrQ XWvOl/Y+wfezY1yZPJ34pLUu9CmqP/eulIUSSc1d2j77Oc6vFWPwDvyJCu9P eYHxhi5ofQUX+6r5CwrwfaCqekeaBi6aks8K2ZQs+j32+Sr4+42/mhXNRnqj 5wVSu2DC4tfan1/h9cOldq0g02ibWEQxqr/oUnf5MCxaOdSh9xrXf1jvdits sI8r/fFmJn7mBYrcfBP0bJ1/58I7fD5VVn0WpGd5FZ2yKEP5ezderVag1fyc PfvfY36LtfqkaP3j/dStcvw850ZrKNF2UTEaGyqRv9VR8JM47XmBM018wvNr KnGbIIOvw+bcKrS/xU9MM3ngwr3Nhe41GA/WmDDpzLyeFOla5A/3Cd0/BYrp M0eL67A/LleZQX95z9ri18CmzvL5xxhkLeypfWnAasTzwH6hpUwKtzrKV3/F +y0X9k6Anvv330BYExvpQz18/1SG1B+OrFnSgvNzVxqPg7WEem7rdzxf/+V9 FCV3zn4ef56L8S/8FauGwYrrD5i3sSlpPr+3UuAjvKj5x663Hc/HYiOzUXhf J0I79Reb+sEgYs+ZFYDiFXPEHDowfrdo1AhotMzvmO5E+O76CvpMsnfdutKc v9gfalc+CoS3/s5w7cLzW/BhjxStvivslGQPPi+l1mUM0uCgsuerXnwfKG95 IUquDX5M+fazqWME0QDsmsCu07Ya6oMYX+XoVUnyeEL71MchjO8sozQNLl4L aQ4dwfzkU0KEyay7CoWLeTPPj0n+7ntXMmDJ45yUljF8nwlY32LSjXD10bgJ 3D8vAz8Buq+M60ROzTy/CSIiV+I9EKk9ZtA9jeuJ+uc/8zz4Lit/g+AgvVmG VCAXGv55MLBWgEOd4fPPXXNrgeuGrGomBTkUSYSrBsr/ALv4LY+yZyGbYD5r 7AEh4kHx20U4qN7dIZ+GwCUF6QNMMQ7Sd854vHvme4V13w6K4/jUkHk/wOtF ltr7mTj+cmvgIPhq2CSqJslB+nDj5toKdJ9FYEeFFAfp6a2w6ZEjRddJlB6X 4SB9VW7Ihx6o4Xw3Y5EcB52HHTcihqHhTvNTTfIIL/xMpNsksPdt9DinyKEq BQm/2/qZwOuYP2WqjPyEUSlnAIREimv8U0H1mbswp8Toy+dvT12dg/DMxXhJ PPjgKmi2nYv8rW7/VIXo13fqC8bVOVQUn7+m0b4Wfsv1TclioXr427Tb/8L+ QpGjLmwOfr5aG4mRomVpTuJaOJ5a+7QZsj4bGxTMQ/hhussqBuCKls9yexdw KCaff+WsTRW079w3oLIQ89vKlfgNvQeFaj5o43ibKq1B6Jpl9Wm7Du6/XrlT B3DyiKzoXYzzB1SKdkF75bfvI5ZwqE4Gsb0NQmBdJViqoIf7nz/9mEmbRa18 k7kM4ztfXNAJDclTxab6qF5Cx/C7GKk79Jr+ZID5Tj96KUDPfyBQ6LGCg/R1 n2w89AWoe1q+GDLC9pRWfgNQVIl4esaEg/RYITk1CSSrS/JUAcJjrXjpLUIK n2HkPiQRnkaSjr84PU1aPKTMOUgv9ZPWxSk4MhSeVUuh/U5VCslVpnseFN/z tsT5P7bwhOlfnsSdsZXILsp6Uy1CN6tQ6bGrUL7wRw91J0FddViqxmqEZ66p zuDByjNF1/NsUH532XMdwuRbM37KKluc7+lT7jSEw2ZJjXbIDlM+mTAJ87NP XN63DuG7acxPm01n73x1Ydoez2dBtUYHyFCdjr+wHuPZSfqJkddryFgtR9x/ 23T3bnD5bGj0840cyowgPoszfoFYczrKdjMH6et6xLr2wsiRyVMtTqheakEP axKEPAQn/ZyRP+xawdy/MHBXyAlBF4Qfnv6AO/M+NAceT9yG/VadzX/grs8T Rxfu4FDdDMJPSO0Z2B5tegS6Yrx5w48HwCbq+CEHd8yvviF0DK4dLfBr80Dn hfBP0pchrXLGDxzeiWxuTIaNHAm8TPaJeuF+3rleKkDrqwX7XPPG/J0j1GfR OrUvvXR9cD8XV3fxoVbMmGfJHtzvql3tA0DNwth90z4O1cMgcs8YPwHyvKM7 OvZzKDE+v/vKjwrIfPTCJdgX1yMx/WAMCnnztkj44fnYapgxDCbVjDan+SO+ xdIGwQLkUG2Q4/JD+LwcdPAUIrtinjuUBmJ+f2svj4J2i9G1W4/g/ghHLhMl v/EMbbuCUL1htR53BOjPj46sDjuG91P3/DgPlns/s5I9jvvn8HRTD3w9d8Ti TgiHkp7mm3qm07CgzsDc6ATCL/4mOTIJ8s4dBhVhuL4hy1IeyLJ8aux6Es3j wWWeJop0+tiQYX8EB+mFDt+PJeirufr6kZEzeAT3oN8cAfLi7kA9pSjs33I4 RIKOUc/XzTqD8dPWfJkCEfWDi8hoDhVCEEGjNxpBcOzyhdUxaF7C9Xb1/gMB Kw/N3xmL+1v2e/U42DuexxmJw/Nz8ENVN/R8PMCKPo/xdjh0DoD9ERsnbS9g e3BjSR84vDH/C/MSyu8WVRcgTp/QUnjy6TK2Sx2FmfTZ4cPxCYk4347C5B5w sbRhj2My5uvmMa8fXEtasUr+KuITHr4sTJzM8ElmNVzD+yeVPPN+lGM8NpF0 A82P3x9Vpgz5Qtzly9ZUZKf92+YpR5Y0FeTNuYXnv/7X29+gPHtOfEs6Wl+U Fm01AOtCQ/akZnCQXnIG80s7bLFvsfK4i/OvD+3mg98aZixOJocKnbk/GKpf QV/fzYmf9zlID1lY1LwLjJXwG+4+QHxSN8GVUrTAJfc8n4eY3wkTJQbN3FUS p/0IxRPxczd3AQUD9p6uXJSPv7uJ1wHVhU9Z5eRhfum2OYLkf1/aNfzyOUgv OuL6wlaol2k1ofcM8Slecm+lLGly7E7D4HOE38pYWilGW9kK5z19ida7v9/A ZZL2c3bHBRXi/ths/T0Ct3SV+RjTOD4xK0qQdqf/s5p4hc/Pnw36w3BvfLQG XYzXDzs7MshAt7/jJ17j+Kp5J0Xo0KV2DdRbXO++845dMIqR/VigFMUT8t+T CDLhMzPubRmO35JmOou+evuAT9QHDjVJEMWKkmXgduCnlTYVqH73W48lZcns VUs0xD9yKC7f3MRw/wh8ppgwXvFpZv64fP6rZYdgcUdffVw1h4rg85cXdjbA Dy82PHb4jPEuZ4xUgs/RebEydXh/5UZIabLZRc6nth7fJ42G+vLk70WBK698 Qfhh6poNI7B3sk59y1eM53l4qAbyPhqMKzdxKBZBffrVNAAEUhPrvzVzKOFp /qV9j/PhbL/R3Ovf8XnJEpt5vshbOMe6chEe/6qUSh9Ul325m9WG/EUsYe4s ekG7ysq2dty/wOOVkuTS/GD1jF8cpIf9tbPsCzA53TTm1YH5VjKeDsOVTqB+ wR9Ub/VpYo0MuXbBjdw/f/F8xImPtwEn3tS5B13ofPPfhf6Vp90+uO4+0MPB +tFRSrNIn6tFlkv6EF7Rkr6gIRiwj6Xe34/nj3WkSpAOASfH8gY5SO+ad0ep Fp6WaKsLHOZQQjP83D69gvHfLXMNRzlUMZ+/7t2CLpj86PY5Hg/jJyS0CZPp 4UK7C8bxenHfMy3wwQYvy5BJ7F9/2ZRJ5rNL55pNo/4RAjrr+8CrwfljfD7u j2qN0wD8HwPsM2Y= "]], LineBox[CompressedData[" 1:eJw90H1MFHQcBvCjA3RwOA6SeJHj7n7IyfEix2/NbMnvUdoyQKcgueF84RSO AjEYtxFgGknIGHoUQ17GrgNFnQOynW1kkQGJCFxTyixoOE5mkm7SdcoBRtd3 rj+eff59nkelP5Ke85JEItnmzn+2faj31h2qTWonW5MGx5Vpu5XvigHyA7F8 ve9jpdsFska0XauL8HLbQjaLgk3Gw88imkUheVGML+Y1PPnfXrFiYlrz2O1K clhYbpqL/nTbRv4quntqJgrifxMXyFlhELeaHxXbxQHSIQpnou3W7ofCQLqE j+qEZuq1J2IVKcEp/xGt5YBDmEgp9BO7vpOOPhX7SW8U/XBCf0SzIPJJH1x+ X5YR/PZz0UP6wVKeP5uwW4KzpD8qzUs7/37kgWpSDsn4PXxTJoUHGYioktzS XVovqMjVuO88847vt974gwxCysx7Rz8tWokdZDC23zfFKBQ+SCdDMTugP36j yxdPyTDEy++EJ+/3QwwZDh/hzJ50rIIfqcBbj7OeqTP9sZlU4m7/IY+sWDmm SBWunBzcp3TKYSVVyPUy3rPZArCXVONgcfkVWUsgckiG9YYYW1r2y0gkI/Fj QKyvceNq3CDX4mp3ZWusNAj9ZBTKPbQ7Rn8PwlEyCj6TZVsLra8ggNRgplPV YK4IxhS5Dg3rQjx7M0NgJqNhaskdylaGop7UIqthr032IBT7SC3m3zznMveF 4TkZA/vMltL+6jWYI2PRvkkXNpYdDgsZh64qo9wQp0A3GY/qzIOpUqcCx8h4 vDppuVg9FoEN5Ho0Rbd2jaUq8TmZgGPX6ppSe5WoIBOwLSzz3M1IFdJJHTYX Du2R16iQTOpgXqOPHHX/ep7UIXLgfOP2PWpoyUSY4vq1t/vUqCcTkevwvDWs ZTCQHPrLfylrTjPkkBwFlRlLKfUMxSSHMcP6i+wz9kKOk07jKVMjQyXJ0b3R tXimjaGH5HB9v3yn8xLDIslhui2rGxxiaCQ5WjoO530yzNBMcnSU2JK3jjB0 khxfBZkWRmwMVpJjMiswb/xnhrskh8YekjxtZ4ggORKsZYqzMwwbSI7XqyZc OQ8YdCRHmqbti4ezDCkkR3G+UjE3x1BKclS88ZHrS4d7D8lR5Tf9U4mToZbk aOrpqJ2fZy/kaD/uafh6wd2X5Li0M2dLxRLDBZLDqr4envQPQy/J0eeIci0v M1wlOf4FAa8q6A== "]], LineBox[CompressedData[" 1:eJwtyX9M1HUcx/EjwAqOBlIkIMf3+CDg8SPINEDh84JPWyToNEQbzIqTXyZC MK4pkBpJeHPYFYxfyugkKGRgtqONfhAhSQhcEworKI3zcpBsGl1ySNHx3v3x 2mN7vpTqwhezH5LJZDtsW7X5mHpNVNbp+BqyM35wQkrZJx3kI6SWr1zpe1uS jnLZ0KqNvLm/2t/Z1hvIDp4fpzl837+R55C9fOJBXu1d/w4+SQ7zh6dmgudt 3Y38meuvthT9aett5Czvvqidyo/4hV8gl3guv9Z4p9jED5KOKDBvNBm6Z3k+ +ShclCeDb0Tf5W6kO864j6j0ry7wOtIT6qk9XzuO/sP3k14o+vakujB4iReS Prj0ujx13Qv/8g7SD/qyQ3OR+2RoJyVUtCzv/vuOAypJJWQTN/FlqSOWx1dl CCrJObJH5YwQcgNuWer3un61Bn+QQdhufu3N94segSBDsPOWLlShcMFeUoW5 y+oT33W5YpYMRYTHpJ94xQ3RZDhcuCVzeuExuJIReH4+/X5AmrvdSPw0kOWQ HuaB62QUek4NvixZPNBHRiHHWXPTaFyLLPJpHCgu65E3edrdhKdyQ40pmY9j A/kMvl8b5qqJecLuZnzRXXE2zNELveQWlDmodo3+6oXj5Ba4TJcmFRiehCf5 LMztytqW8nW4QUajNsTbqTfNG+fIGOiacoYyJR+7sUiv3W+U3/bBS2QsFp9r s7b0+WKe3AqTOfHIQNV6/E5uw/m4KN+xTD98QMahq1LjkRuuQDcZj6q0A8mO FgXKyHhsntZ3VI35I4TkaNh4tmssWcI5EjjeX92Q3CvhGAns8E1ruxqoRBKZ gISCoQwPrRIgE9CyXh04alFCTyYg8PJHdTszAhBAJkIXPqAa7wuwm4icBadr wyqGLFJAfekvSfsuQwYpkF+Rurz9PdtPCmhSDdflNQxvkAKnLJozujqGKlKg O8b6oL6Z4QIpYP1mZbK9k2GRFNCNy6sHh5hdgabWw3nvDDPUkAKtJUaRNMLQ Tgp85qVbGjEyGEiB6XTPvIkfGX4jBYJN3mLGxBBICkQaShUfmhk2kQKxlVPW 7NsMW0mBlODmT2bnGHaRAsWHJMW9e8yuQPm2t6yfLjAcJQUq3WZ+KLEwaEmB houtpxcXGepJgfMnnHI/X2LQkwKdu7MTy5cZPiYFDAFX/OL/Y+ghBfoWgqwr Kwz9pMD/gFAtQg== "]], LineBox[CompressedData[" 1:eJwVkms0lHkAh5WuouMShlyGd1BjhFZKLu9vjI3B31ZShy4yrrsNljUqXUgK XaxiJa0VSVvWpXZql0p2skllOi7hIJXJdpIy0zQx1Nr2w3Oe7895rASJG6Nn a2hokC/879KDgnnOUce9VENtLazjYq+WLmbgFua3dNcvjL3cvtP0zL2mw0zm Xppr+FjA6KugS5tPWs5l5tKp66/0avZdo4WeovgJy7O0wTvj0+peCd01HVco t7xMv7gVlPiht5OePzBs99aygfZhjT5V9A7T5Q/Kkt5YttHq3tU/yXvf07V1 uQPCFf20hHepsqNCE7F0x9mxZBnNeNbwj4Cjg4SR5TJx7WuaIQy/Mp9nAC2r LLtna+R0kfO6m0EhDOTpPmSX71TSg8VOzQpdcwgGNt3RfPSRzq1MfzzbxApJ f2cJEu2m6CWFstyCUgpXv9cOZvA/01mb+F6dH21Qvm/XqNMWDSS7lYe3ZS5D ZtmnDR/GZsF3fCotQcaGRtdz3ErTxFGPDRGmaxxgmxKzZxN7Llxqz4oP3nHE S9WZzYtuz4NwUpFxX8cZ/iPfHTidtABKe90hh5CVCHqZb29hoQXP6t/OFxV9 hdG7goz7NYswru+/c7PEBSv0esx54TqQndi5OXm+K7RoVcSgcjG+Gd/NH3Fd Dd+3YRPWIboYi1zwgzh9DfokUbPCOHrwYRnPzpa44XpOyw6mSg/a7bZ59eNr ETNX9Fwq1YdRTt16V1cPRCbvu65dYoBj9m66BrGecIy1lwZGLEGbKXeV8pQX HutzFoncDOFpJsl37KFxszbzHEfTCDqaFSkRmcC+Wez1j54awfSQpUeoLRda g2l+CWJjaNlsu7GxlYuRKqvCsv0McDxN6nZv90bhMpM5DSEmSB3Sv+uvwUN+ SUxrBNMU75QnQvjFPIQVbpdqvzKFu+O9Er6DDyZ9LqrLmpbid6X79ITUB7IR 7z2SbDPEcFb2d0R/jQpP56XtEeZwexfVHbpwHWqOiPRiHSzAZzGITsU6ZIdE BmiqLMDKOLZHstoXqwbLL2e3W4IT7XbHpt8XxcvP1bQHMBHeFJclTvJDevPJ 4oAGJhrPd0cpDPkgS0MuPmBZQf7rzITjH3xwE1q36uVaIdqmemEJ8UeZmYD1 SGUFBbvA9ZrcH6y7l4qCtlqjsXL6hSonAPkOEnZnkzVCfSi4WwQiRjmno41N wTA+u2FFcyAEV98zc3+kYKAlvEq2EAgzgz/5n6JwiXcgTR5KIAoW92oXUHA5 kMcr2EaQoxLl5RdRgLz+SV8EQa2bevrMl2+P9ajUkUIC9V8zPVXVFN5XpHun HSLI79Q+2dJKod+9oKuqmqDkQnzc0TYKMaLKn/m1BBdSpDy/hxQma69Hj9UT 3DDKn3oopcCw7ptwvkEwGGYQ1/WEgu8Cc7PbzQR2MhPesIzCre6qqK4nBE7i NIvKEQp+i/90SO0jWHtkQB39isKQb9tHxgBBoF1p/etRCvLGNzk7nhMk72Ja KBQU2OVONa9HCfZ7HFJfU1Jo7uemnnhLcERnuDtFRcFrSTDtKCcorrtwfHKS QmK2qCNFRVCRMSe2cYrCaPPREuNJguoN0d77P1HImDoT2ThFILa+Z+7175ee Lpc52z8TNClt1TMzFKriG1UzMwT/ARAYLPk= "]], LineBox[CompressedData[" 1:eJwtyn9M1HUcx/EjwBpgEykSkeN7fBiHJxisdGrB5wWI8jvgI7nhKjn5ZSAK 45wBlaGExLDTGHIYXYjSSIF0yEYmGZKEwDWh7Ae0GOfFINw0uuSAInnz/eO5 xz9PlfZgcsYTCoUi/nFL1r+jXRGcXhlqIK+F9gxLcbul/XxZA1+81XVMkt6S beb1N6q8HaUK/jHZyXNDdAceeRt4DtnHh+ezqx94N/Mh8hf+5Mi4+r53J3cg J3nDbWP+n4+/86SNt7ZVjORu/JW3kU7I4ncM0wVmnk26Ic+y3tzeOsmX9YCT 6rj69y0P+LISTq7q1zTsneGVJIN2ZNfX9gP/8L2kH/K/Pa49qJ7jh0gNLh9y EWui/+UdZCAainOmgnYrYCSDUGpcSPp72g5lZDAUw2P4qsge80NLvgC/wswj uzSO0JCbcM965lXn6yswQW5GjOXNt0/nP4VocgsS7uk3KJVOiCe3Yeqm9uh3 Lc6YJl/CRte7XhFvrIQ/GQInbk0bnXkajmQodt5PfeSTsgqRJPBzd7pdaoCr bBiunuh5XbK6ooMMQ6ajbsxkWo10Mhz7CoqvutS5YT8ZgeezNpji0p6R3Y7v Vwc467Y+i0EyEtdaS88G2LvL7kCxnSZx4Dd3HCZ3wGm0KCqv/Tk4kzthaVJV G0vW4A8yCtX+Hg6dKR6y0dDXZfamSWtRRcYgtfo1k8vEWqSTMZjdfsFm7PKE InLJWJgt4Ue6y9fBQsbhXEiw52CaFz4h49FSpnPNClTiEpmA8pR9sfZWJT4g E7BptKG5fNAbL5KvoHb92ZbBWEk2Ee/eqKqN7ZRQSiYi3jPlwm1fFaLJJITl 9e5xrVCBk0kwrtP6DlhV+JRMgu/Nz2oS9viAkcnQB3Zrhrp8cJpMRuaMw50+ DUMWKaC9/JdU8SFDGimQWyoWYk4xWQGdaP/J5SOGw6TACavupL6GyQq0brXN n6lnuEQK2L5ZvNt0kWGWFNAPuVT19DKcIgXqGg9kv9/HYCAFGgtNEVH9DEZS oMNdP9dvYrICo6lu2cM/MoyRAmqzR8S4mcGfFAhqL1KetzBZgW1lI7aMCYbN pECcuv6LySkmK1CQIykfPmTIJwVKXn7PdmWGyQqUrRz/odDKcIwUqG1rrJyd ZaghBc4ddcj6co6hiRS4mJQRXrLA8Dkp0O5zyyv0P4YrpEDXjJ9tcZHhOinw PzlvMTQ= "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotRange->{{0, 10}, {-79.99999836734693, 79.99999836734692}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.4703117682274046`*^9, 3.470315063915637*^9, 3.4703723995123315`*^9, 3.4722919412795143`*^9, 3.472294168844879*^9, 3.4722942000513067`*^9, 3.4722954044984417`*^9, 3.4722975754648*^9, 3.4723013403064003`*^9, 3.4723141641553173`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{ RowBox[{"In", " ", "the", " ", "Non"}], "-", RowBox[{ "interacting", " ", "case", " ", "the", " ", "value", " ", "of", " ", "J", " ", "gives", " ", "only", " ", "the", " ", "global", " ", "energy", " ", "scale"}]}], "*)"}]], "Input", CellChangeTimes->{{3.472311796715655*^9, 3.4723118325416546`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Ground state", "Subsubsection", CellChangeTimes->{{3.4722942610373063`*^9, 3.472294262547306*^9}, { 3.472294986630659*^9, 3.472294989333929*^9}, 3.472311839339655*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], "]"}], "^", "2"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.472294524455306*^9, 3.4722945263103065`*^9}, { 3.4722946909733067`*^9, 3.4722946989573064`*^9}, {3.472312465580655*^9, 3.4723124655866547`*^9}, {3.4723140542453537`*^9, 3.4723140573502855`*^9}, { 3.4723141763879857`*^9, 3.4723141765070214`*^9}}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7CHsAnuogAOEvwDK53BgBtN7oHwBBxYwfQbK F4Gob7gI5Uugycug6VdAM1/JAdX+DzB3wIADKpcDjS+AxhdB40ug8WXQ+Apo fCU0/uAJHwDJIB7c "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "8.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{ 3.4722945283993063`*^9, 3.472294699889306*^9, 3.4722954045574474`*^9, 3.4722975757144003`*^9, 3.4723013404624*^9, 3.4723118528556547`*^9, { 3.472314164518426*^9, 3.4723141817515945`*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Compare Atom number distribution in ground state with a binomial distribution\ \>", "Subsubsection", CellChangeTimes->{{3.472311946356655*^9, 3.472311946516655*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"norm", "=", RowBox[{"Sum", "[", RowBox[{ RowBox[{"Binomial", "[", RowBox[{"NAtom", ",", "k"}], "]"}], ",", RowBox[{"{", RowBox[{"k", ",", "0", ",", "NAtom"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{ RowBox[{"binom", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"k", "+", "1"}], ",", RowBox[{ RowBox[{"Binomial", "[", RowBox[{"NAtom", ",", "k"}], "]"}], "/", "norm"}]}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "0", ",", "NAtom"}], "}"}]}], "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.4722946417583065`*^9, 3.4722946432853065`*^9}, { 3.4722947118103065`*^9, 3.4722947369923067`*^9}, 3.4722948380498023`*^9, { 3.47229486922692*^9, 3.4722949100700035`*^9}, {3.47229545788478*^9, 3.4722954589808893`*^9}, {3.472299973138*^9, 3.4723000031991997`*^9}, { 3.4723001064088*^9, 3.4723001230228*^9}, {3.4723001544568*^9, 3.4723001863120003`*^9}, {3.472311860556655*^9, 3.472311934143655*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"{", RowBox[{"binom", ",", SuperscriptBox[ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "1"}], "]"}], "]"}], "]"}], "2"]}], "}"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "1"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4722942951493063`*^9, 3.4722943393453064`*^9}, { 3.472294418821306*^9, 3.4722944314043064`*^9}, {3.4722944801783066`*^9, 3.472294488545306*^9}, {3.472294563413306*^9, 3.4722945809243064`*^9}, { 3.4722948550525026`*^9, 3.4722948609570932`*^9}, {3.4723000878292*^9, 3.472300093024*^9}, {3.472312465590655*^9, 3.4723124655956545`*^9}, { 3.4723140635361404`*^9, 3.4723140656157637`*^9}, {3.472314187399288*^9, 3.472314187526326*^9}}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAwA2IQDQEf7CF0AZRmcIBQC6B8Dih/D5QvAOWfgfJFIPyG i1C+BJq8DJp+BTTzlRxQ7f9gz4TmHiY09zCjuYcFzT1MaO5BlZdB06+AZr6S A6r9sPCBAwdULgcaXwCNL4LGl0Djy6DxFdD4Smj8weqe0fQDcw/MfgCJPjva "], {{{}, {}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{28, 1}], LineBox[{29, 2}], LineBox[{30, 3}], LineBox[{31, 4}], LineBox[{32, 5}], LineBox[{33, 6}], LineBox[{34, 7}], LineBox[{35, 8}], LineBox[{36, 9}]}, {}, {Hue[0.9060679774997897, 0.6, 0.6], Opacity[0.2], LineBox[{19, 10}], LineBox[{20, 11}], LineBox[{21, 12}], LineBox[{22, 13}], LineBox[{23, 14}], LineBox[{24, 15}], LineBox[{25, 16}], LineBox[{26, 17}], LineBox[{27, 18}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{37, 38, 39, 40, 41, 42, 43, 44, 45}]}, {Hue[0.9060679774997897, 0.6, 0.6], PointSize[0.03], PointBox[{46, 47, 48, 49, 50, 51, 52, 53, 54}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{2., 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "8.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.4722943212993064`*^9, 3.4722943402893066`*^9}, 3.4722944896643066`*^9, {3.4722945573333063`*^9, 3.472294626198306*^9}, { 3.472294778391837*^9, 3.4722947982558236`*^9}, {3.4722948456715646`*^9, 3.4722949163746343`*^9}, 3.4722954046164536`*^9, {3.472295437372729*^9, 3.472295462837275*^9}, 3.4722975758548*^9, 3.472300033276*^9, { 3.4723000946776*^9, 3.4723001904772*^9}, 3.4723013405559998`*^9, { 3.472311927597655*^9, 3.472311955636655*^9}, {3.4723141645634394`*^9, 3.472314188717684*^9}}] }, Open ]], Cell[BoxData[{ RowBox[{"Perfect", " ", RowBox[{"agreement", ":", " ", RowBox[{ RowBox[{ "The", " ", "atom", " ", "number", " ", "distribution", " ", "in", " ", "the", " ", "Non"}], "-", RowBox[{ "interacting", " ", "ground", " ", "state", " ", "follows", " ", "a", " ", "binomial", " ", "distribution"}]}]}]}], "\[IndentingNewLine]", RowBox[{"\[Rule]", " ", RowBox[{ RowBox[{"As", " ", "expected", " ", "for", " ", "a", " ", RowBox[{"State", " ", "~", SuperscriptBox[ RowBox[{"(", RowBox[{"a_l", "^", RowBox[{"+", " ", RowBox[{"+", " ", RowBox[{"a_r", "^", "+"}]}]}]}], ")"}], "N"]}]}], "|", RowBox[{"0", ">"}]}]}]}], "Text", CellChangeTimes->{{3.4723119613176546`*^9, 3.472312048641655*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Excited States : NonInteracting", "Subsubsection", CellChangeTimes->{{3.472295004659462*^9, 3.472295018192815*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\n", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"ImageSize", "\[Rule]", "200"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ SuperscriptBox[ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], "2"], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"ImageSize", "\[Rule]", "200"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.4703142380796356`*^9, 3.4703142449276357`*^9}, { 3.4703142767176356`*^9, 3.4703143025326357`*^9}, {3.4703143358026357`*^9, 3.4703143585206356`*^9}, {3.470314794314637*^9, 3.470314864262637*^9}, { 3.472295036965692*^9, 3.4722950397889743`*^9}, {3.472312131445655*^9, 3.472312143632655*^9}, {3.4723121790796547`*^9, 3.472312180254655*^9}, { 3.472312465599655*^9, 3.4723124656076546`*^9}, {3.4723140741573257`*^9, 3.472314076701089*^9}, {3.4723141940742903`*^9, 3.4723141941703186`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7BnB9AZ7qIDDOev6tHkLjkH5HA6vf1xaWa91 FcoXcPC2zxB89e4ulC/icGf9GvbNux9A+RJo8jJo+hXQzFdyQLX/g/2smSCw E+4eVD4HGl8AjS+CxpdA48ug8RXQ+Epo/METPgCJtXil "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{18, 9}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "8.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7CHsAnuogAOEvwDK53BgBtN7oHwBBxYwfQbK F4Gob7gI5Uugycug6VdAM1/JAdX+DzB3wIADKpcDjS+AxhdB40ug8WXQ+Apo fCU0/uAJHwDJIB7c "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "8.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7M9Y16fNW3BsP1TA4T8YXIfyORw87TMEX727 C+ULOLz8cWllvdZVKF/EgQEFSMDk7SF8GZh+KF8BZj6Ur+QAtd8e5h5U8xjQ zOdA4wtg2I/Kl0HjK6DxldD4gyc8AEn8Yhs= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "6.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7P/9B4H59lABBzD3/0Eon8MBQp+B8gUcIOp3 Q/kiDgwoQAJNXgZNvwKa+UoOqPZ/sGdABWjmc6DxBTDsR+XLoPEV0PhKaPzB Ex4AYqNkIw== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "6.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7F/+uLSyXuuqPVTAwdM+Q/DVu7tQPofDv/8g cB7KF3A4Y12fNm/Bsf0QvohDYPQtqwifm1C+BJq8DJp+BTTzlRxQ7f8AcwcM OKByOdD4Amh8ETS+BBpfBo2vgMZXQuMPnvABAPDVaEQ= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "4.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7P/9B4Hd9lABBwh1BsrncPgDll8P5Qs4QNTP h/JFoPzDUL4EmrwMmn4FNPOVHFDt/2A/ayYIrIS7B5XPgcYXQOOLoPEl0Pgy aHwFNL4SGn/whA8A2s2akQ== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 4}], LineBox[{15, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{14, 5}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.05}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "4.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7D3tMwRfvbu7Hyrg8PLHpZX1WlehfA6HM9b1 afMWHLOH8AUcIPQNKF/EgQEFSMDkofplYPqhfAWY+VD9Sg5Q++1h7kE1jwHN fA40vgAaXwKNL4PGV0DjK6HxB094AAC7PEo3 "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{14, 6}], LineBox[{15, 7}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "2.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7CH0GSjN4PDvPwjshvI5oPz5UL6AA4Q+BOWL ODCgAAk0eRk0/Qpo5is5oNoPcw8coJnPgcYXQONLoPFl0PgKaHwlNP7gCQ8A M/JMPw== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "2.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQB2IQDQEf7O+sX8O+efcDe6iAAwMK4HAIib5lFeFzcz+E L4AmL+IAMesGVL8EmrwMmn4FNHklB1T7P9ijynNg2IduPrp5qPzB4z8AvmMx Sg== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 3}], LineBox[{13, 7}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{12, 5}], LineBox[{14, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21, 22, 23}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["0.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQB2IQDQEf7MHshov2UAEHBhTA4QBRewQqL4AmL+LADKYP QeUl0ORl0PQroMkrOaDa/8EeVZ4Dwz5089HNQ+UPHv8BAA2cGFQ= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 3}], LineBox[{12, 5}], LineBox[{13, 7}], LineBox[{14, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21, 22, 23}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["0.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7D3tMwRfvbu7Hyrg8PLHpZX1WlftIVwOhzPW 9WnzFhyD8gUcIPQNqHoRBwYUIAGTh6qXgemHqleAmQ/lKzlA7beHuQfVPAY0 8znQ+AJofAk0vgwaXwGNr4TGHzzhAQB7PEo3 "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{13, 4}], LineBox[{15, 7}], LineBox[{16, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{14, 6}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["2.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7CH0GSjN4PDvPwjshvI5oPz5UL6AA4Q+BOWL ODCgAAk0eRk0/Qpo5is5oNoPcw8coJnPgcYXQONLoPFl0PgKaHwlNP7gCQ8A M/JMPw== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["2.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7F/+uLSyXuuqPVTAwdM+Q/DVu7v7IVwOh3// QeA8VF7A4Yx1fdq8BcegfBGHwOhbVhE+N6HqJdDkZdD0K6CZr+SAav8HmDtg wAGVy4HGF0Dji6DxJdD4Mmh8BTS+Ehp/8IQPAPDVaEQ= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 2}], LineBox[{14, 5}], LineBox[{17, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["4.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7P/9B4Hd9lABBwh1BsrncPgDll8P5Qs4QNTP h/JFoPzDUL4EmrwMmn4FNPOVHFDt/2A/ayYIrIS7B5XPgcYXQOOLoPEl0Pgy aHwFNL4SGn/whA8A2s2akQ== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 4}], LineBox[{15, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{14, 5}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.05}, Frame->True, ImageSize->200, PlotLabel->FormBox["4.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7M9Y16fNW3BsP1TA4T8YXLeHcDkcPO0zBF+9 uwuVF3B4+ePSynqtq1B5EQcGFCABk4eql4Hph6pXgJkPlVdygNpvD3MPqnkM aOZzoPEFMOxH5cug8RXQ+Epo/METHgDJ7WIb "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{12, 3}], LineBox[{14, 6}], LineBox[{16, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 2}], LineBox[{13, 4}], LineBox[{15, 7}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["6.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7P/9B4H59lABBzD3/0Eon8MBQp+B8gUcIOp3 Q/kiDgwoQAJNXgZNvwKa+UoOqPZ/sGdABWjmc6DxBTDsR+XLoPEV0PhKaPzB Ex4AYqNkIw== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["6.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7BnB9AZ7qIDDOev6tHkLju2HcDkcXv+4tLJe 6ypUXsDB2z5D8NW7u1B5EYc769ewb979ACovgSYvg6ZfAc18JQdU+z/A3AED DqhcDjS+ABpfBI0vgcaXQeMroPGV0PiDJ3wAtTJTng== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 2}], LineBox[{13, 4}], LineBox[{15, 6}], LineBox[{17, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{12, 3}], LineBox[{14, 5}], LineBox[{16, 7}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["8.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7CHsAnuogAOEvwDK53BgBtN7oHwBBxYwfQbK F4Gob7gI5Uugycug6VdAM1/JAdX+DzB3wIADKpcDjS+AxhdB40ug8WXQ+Apo fCU0/uAJHwDJIB7c "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["8.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.4703142457686357`*^9, 3.4703142804636354`*^9, 3.4703143598696356`*^9, 3.4703148022476373`*^9, 3.4703148328246374`*^9, 3.470315065075637*^9, 3.4703724011970344`*^9, 3.472291944862514*^9, 3.4722941707880735`*^9, 3.4722942274573064`*^9, {3.4722950317381697`*^9, 3.4722950429802933`*^9}, 3.4722954047444663`*^9, 3.4722954706650577`*^9, 3.4722975761043997`*^9, 3.4723013408056*^9, 3.472312148143655*^9, 3.4723121814346547`*^9, 3.4723141647735023`*^9, 3.4723141959328475`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{"Left", ":", " ", RowBox[{"Amplitude", " ", RowBox[{"Right", ":", " ", "Occupation"}]}]}], "*)"}]], "Input", CellChangeTimes->{{3.4723121592366548`*^9, 3.472312170825655*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Interacting case", "Subsection", CellChangeTimes->{{3.4722950516681623`*^9, 3.472295053377333*^9}, { 3.4723122109736547`*^9, 3.472312211877655*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Energy", "[", RowBox[{"2", ",", "U"}], "]"}], ",", RowBox[{"{", RowBox[{"U", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470311789402405*^9, 3.470311805185405*^9}, 3.472300774198*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwVxXk01AkAB/CxKDtkjVs0fuMn5JooJa/8vjleYpQj1RKZGYOY0bLYmo6N SCqaWnKUJykpzxlZtem3EcmxSVHRbpJ6OV6OnXJtdvePz/twBPv9RN8wGAzv //x/wVHBEruw085mN1ywuMilm3sI3i5iH/XQXOGW6jMuvdjSeJwgDlLxCQul RCmXLqAzjJWJdGqv+2yp0IdLizclSL4Y51FnclsHPYts6Z75yKwJ4xtUqa+U SnOzoZf2vzUfN26g7L1UHPVllnTR48LYUeM2akTq6vhw/Uq6ojK9X2z7ijrS u7vKt0yLjqC688bihqjrvFMuOprPqJjhVUO1FR+p2MnE6g+ZOmByUsz/cpyg bl5xdLpbuxKZGu2WRaHT1K3z/OCkPi4E/TvuK3Z8pr6VqSsMCxwQ+zBFsN98 jmrOnkp5cscJ1T+o+etv/YdSHVcOPF5DoehQ9MjqXQwsa6ST7p10QXLhgu/f Ywqg1zl9GlZxB6PnDX6TKmI0tfKL/qEtMIsPP7DDUhnJbtk/W3A88U6es1P1 3hLYj3yyqMzlwXM46sj5WBU4N11L1HHbjm3vZFZsNhP+e8Zk8gkfjDQJjj0q V8Wp+zXlry38YMvqXeG6dxnOlLDt66X+YFJy/sC0Op5XcN1v1u3AlvHALyYB GjhmqhCSztyJFw/CFAKtWXCekXo/3b0LdSebQwg5C25t95yCZLsRrpzwpqtL E4/Vddjtg99DGHeoTi1fC3UaiS/OGAWBG2HVxeNrg1HfJx3w2YM/NK1VEzbo oMWTalcrDMbdiuSL1oq6WEPf/7W0NwSHFCx9Ol7ros92jd932qFgDkg9Ymr1 UMa0q8pqCMVwCSer8LA+DC/pvn/lz0eWhYFSQ4ABmv0ImjnPhyw/vJVPLIez R+wQI0eAwKzgLrUPy1H1Riu0gyvEjNu12cJGQ7hn9nocfS7E0LDLgQdpRujt zZ35uj8MVzbZGXbyV6BaxLUR6olQnprAirBhQyjul+XfEiEtQOilKGeDSIRb OS8cDgNFN9I6jeG3kpl5eSocuasulnd6EagXrFePyYjAz3RGrlcDASvvvvMG DpHwNgy49tiUg0t5DpeKXkZic0xrECudg5wnPG/mj/tQaCQw7ZBzcCRIGLjN IAqmTdcvbAsywVUHvYDE2ijIbB5YPm00AXPiRVgSLxrh00rdbZYkZuhkgWgy GoLqKSL9LIn06pTL9qfFECf7L3ieI8GIuE0NZoiR4F/bp/YLidbSxtdnZWKc lCdkyi6Q+DPCX3c8W4yKDbPzOQUktk+dO3j9shizvy/2lpSRiNJOUTG6LYbs qVpGcyuJpXDZqjQoRn6xJPJEG4lp7cymmiExiuO7XD3aSbA4dRv578W4rSub a+8i0ROXbdU4KsZAoFZkz3MSi8rF8z99FsN8yMD17RAJibmmaFRVgtW1UvbV YRIf600689QlcErtnxV9IJHRobHWgyUBz7yg6uMIiYvaJ75e1ZUgLppgT06S UCVepoZwJDi8MWm2ZppESffLd2qmEqQue/ssXk6iyarB5a6ZBLmVxadnZkhw o7Xn9awluHJMKeLOHImAPFlAi60EZb4il8MLJHIUxiri7SSoNWlZ4fyVRPAj s6XkWgkap81mFxdJzLE2h3Svk+BfKy0njw== "]], LineBox[CompressedData[" 1:eJwVxX08lAcAB/DzWuMsL1E67sVjLirL+lh5qecXvUhOdGTR252XU7h7GBVO a5VQeVnJW12GSB95KaqxxcWNvG5SalETWWp6taND3bY/vp8vRyjZGqpJo9F4 //l/2SGhrkPIyTW3+HxDtZorV/SxvQLYe8m2TN4b43auXN3aeJTNjie7up7q O5/mymXydJYOO43MmdH2vG3NlUeujouaYuWTuSdEc6s9beR9M+HZb1mXycn7 5THD+dbyOQPD3FesetIloeFGzjqOvKijMPpvVjvJosss/kgxlVdVpw1E2j8i b94XTXJcJkkR2Zs/HjNCFjcluuiOWUI8ajtSV/WClL4nysVn7aDHOcb9c9Vb 0tuUFeEWvwIZhp12RXsmyEkLr+ILNk4QDvg1aXVNkgy6+XJ7JxLRvx4TSrjT pKvJgmfOmW64StH5Czd9JK0PxPY/8ViPosSIl8sDaGhdUTuSt9IDRwpnff8Z 18C271zd773xBK1vCL8kaGF6e63qUg4PNrFhB/3sdBBec1az28kHz5S52/Rv 6cLlfGaQZ4YvPEf3JZ2OnovujlXZsx+3wvtZ1hImUw877qi/uBXqh5ctwsN3 KvXhMn7qiWedP+yN+i3ddxvA2faokSszAHqkUjA48TlKEobn8yTfYOOrwCkr f0PclCoOdA9sx8PmEI3ApUbISC26o7E2CNdTFbvYSiPMXLPqu5m+A2E6cUM9 PcaYGim5/lq5E8ExidfpBSbYYXgwsHf9bnwpWtLjJZgP6QbTxl0b9+A346X6 cU6mGP2xpDRftQc/Vx05t1TLDH1ajNcthQIkatj5dD02g+XjClEtXwi9wQQP cd0CKAYcaY7awRgt42QXSheCe1WQ8FN5MLIXm2vX+5tj8C96lWZQCLIKwtoE 7EVg2TZZBWiEIjB7Zw/9+SLwH7hd8b4Yig/rSlWFjQyMZ1ocMvAPw8io28Hm FAuUNW3a/1QVhuLVDoxugSWCFSZW0isiVCbHGYmWMfHtriQHB344UvyDN2sp mVh5RiY4PRkOx8GiyyndLNQoLjg2XNqLPNtzld2b2ZALNsZr8fbhO3l63uZ6 Nk74DMiNaRHgMfxLO6w5EJTud+2tjsBacVuQURoH9sIhxQ1+JAothNZdSg6S 45M0hTpRsG65lOMdZIXnununv66IQtayZru7jVYY875wSs4TI2xCu7fdjoD0 iS8175MYwqvv2WmZBLQjVX0niyWIPMKf9fyBQNYqU6d9pRLE8ese0M8QyMd5 mUe5BKnKuIysHAKVBeMhOlUSVDmpZnJlBHi5BeOH6iVQ3Vb3l1UQ2J3hNRT9 uwRZd+npijYCDa30wIBPEhSURIUfbydwfEVkfwGNQklsj7tHJ4Gp92nqzzQp 3DDLmu7sIbAp9ZXPmDaFwUCT8L77BJLmBLy9qEeBO2LuPjxCYHZRC4dpRmF5 XQLz4iiBCb+aDekLKDgnD6hCnxN4KNsWMbuQghdXVvPiJYHUkp7aRwwKMRFs 5rt3BD6KxWtzORSkrt+rrk0QmGNkE6JLUEg2GL4XqyRwbkvu8ThrCnnVJSc/ fCDQOVbWwedSKD6sLWqYJpActn68eTGFCt9QN+ksgXltMoOv7CjUWbVarvlE YIxRY1+0hELjhI1KrSaQvV+6xXAZhX8BWN0rYg== "]], LineBox[CompressedData[" 1:eJwVkGs0lAkAhhVqG+w20xJhZvgs0rDsKZkuvjfa5FqaUKSYcb/Np23OWiNJ rKREKynJypZKRhc6R9lpElm36aKLXUMdk1y7WE0uxaz98Z7n1/Pjec34wm3h 8zU0NLzn9j9LUvkLHMJynD9wOIoZNUvW2Mn2CmBHkz2fcyIT01ky9QPpITb7 F9K+avo7HW2WrER2jKXNzibbpDms6zSmLG69KH6CdZrkDYlGmpaayDo/RxV8 YF0mmwcm67W5hrKF3X1Wb1l1pLrClbX+1GJZWWtp4girhRSoDS7fqu2+K6nO 7o6z+4c86e/wZsWYCSLJx6dH9yrJQsHziQwGBwn9y5U1kiHyh9l7gyailaCZ ZVi9dPpAGjX2KUZWrUXu4jabspBxktHlKem4CvC7t9/VbP9EHmFnne8bdUVi UwZfaDVNftPqYaGv64brlC7P0H2GZLQUdVgMuKNMHDtsH6CBqdhg1yNjXkgv /eL7cXQedo7bbDOs3wKNzleoT9bEwdvu/W6rfWG5LyJpu4029HMNXqsvbcNr 1Sl/nT8XYIv54EvDWR48+mP2n0j8ChUF8gnvOD/4vM5bwWTSsEBc597zyB/D 9/lpf1XpYDBGI3Gt8Q7Y0Z+buu7RQ6++T9C5AztBI1WhivGvUXhPdrGpNRBu bwMnzP0Wg+VkSnOz34WuhrB5gRw68q3fa9vlBqP2cONutoqO2YXRAfLO3YjQ Fr2Syxm4HSeV05eFQLBXXKt7ZglmH/3+4yZpCL6PXCH3Cv0WMwNew7Q9oXjI 4OiIuPqY+fun9g16fNyRpBdzNA0wmNXUKanmQzzPZmt7jwFUzu/eFO4RgKZI 3pxQsxS9jgEMW90w9F80KyhNMcS7xsAeRlUYCqyNtOr8jOBkKjBMDQpH3pmI 5lD2MlQqQh+6zIYjsCBYrjuwDEph8ZuWkghMbrwwVSo1xsmupzMKj0go+12S GrJMEBL0sx9vNBLn1zsYd4SaIm2V5NmO4ihUZYrokbZMKJefzWxyjkaWn8BT U8XExkf0jzO90VilKLuc1cFC8KaylJajMShaXlzV4cnGoslrN9V2sTggO1bk WcdGFiPPpa03Ft7GfhdaLczge6NSFJEThw0JzUH0bDO4iDNfxHPiUWrCt2hX mcHV/+ouve54WNyvKPQJMkeCUJVklJqAPNsGmydSczSwVEafTIWIGNd63GJD YK1NpWV8mxD86/+ys48TqL+Zz73kSCEunffFI59AqmWShO5EQcSreaH7GwET VREh5lI4rBLl5hXO+Q3ZX/usoyDhTn0+VUIg/pX1wPgGClP31M8vVhKYzxWU k94U8p7oHmtsJlDKm3B7IaBwpjw+6tcWAqcTHRsRTqF8n9x1cxuBDNk1XImg cMsgb7pNTmARLWDN/mgKisAlUZ3PCByYjLEnhBSslEaufUoCQydqrYTJFOxr kpl/9BM4dPZKRZeYwprM7qnwAQKFq7utXPZT8LIquTY0TCCc+95aP43C3lg2 c2yMgLme0vZOJoWUdQenbowTWLqxttoii0KmXt/TfSoCYWvuO+QeplBUXZ4z OTn3h/iEY2gOhfNpWpG3pwkkPebVtR6lUOkb7pLyhQB7Zuu6lbkUaswfmDrP zvVrHblbcpyCdNxySq0mcG5k1mVhPoX/AILNMzk= "]], LineBox[CompressedData[" 1:eJwVznk4lAkAx3EySY4p2ZRkZngt64yOfUrp/ZVK5dgQMh0YDIVxvDNtji2r bGwPjdKBnbWSzmcojUpZzapRiiFDWaPNQ3g6PMxqYkyx7R/f5/Pv15qTFBgz S0dHx+9r/ys6zNF3jz6x/oTMiaudmSd9pGD5hrL2kyHiO15aFV0609RwlMVK I+/zFvId3phIRdJ85mxWHplKdywwazaSJngKEieYxaSsgrbI/cwcqUIbVzTG vEpWHwtRufGmH8xR9tuPMOvILXbKhebVMrL8aVnKe2Yzue7+xVdN/fNRVZ2n THDtIdsiRZZDTg6IJZ8Xf0gdICmHONkK1QrwBh0GJFVvyQyblJtMhQcMrY/Z v149Rh6tGSstmrUBBfOfOZZHjJP+L5N8L3tvAke584FeyyeSLUnbpmz0Rors GCfJforsutI3VUb44GaycdDibV/IXIfRVeJN/ijPiH/nFqoD5xK/nraOHcgu +xzw8YMulu07zM6NCYSOog/16Xrwi9vb2joaBDs+99BOx9motl0c41cajDfq cyFGf+ojbVve7SWOodg+eOCnUykGqHRQZMf37IL/G6ETg2GIsff720az2Xj3 kJP1RGyEgqBJHS19D1xNX1h5hZtApHuQJqnfC0NSHdk7TkfhlS2nJ/zC4T3C nrAJno+JCAvP9KwIdDdG67KdTbF2xNXAMiQStbmP9rHUpmC59azIsOKAO1vQ J5cvgDD81Jd7ag6iUjNqjUvMEB3oUlX7IArLYp3kvpHfIKWTrW3OiUbbAmcj wZqFsDCJVDbsicH9quxSZz1z3Ph10jf2Wy4ydB13tLwyh9mptbaqaS4Me9O3 8iSLoI3aEF3YGYvBS9ZFZZmL0VVJ//uf0jgUfWdBqwu2wBDd5KMJfz+EJdzH kawlONgjsB32PAB20V658fASaAIeCtr14jG5qVJT1mAJrSjsWmlPPAYGNx5q PL4UCk13oXFFAi54ulu2RlrhiFVzZ3hmIsQ5AtNYFwb6Dq8rDvHm4XhwlI+e moFbdwf6w+hJWNVbfvV4KxMd6UYycigJ5x1Kxa0+LGyua5o7EJqMI9L88z51 LIRfX1q9SJYMP8vgyqe21siN4U0EuKVgA+/xbtM8a5zpanfbXZSCsqUc2xa1 Nb7PdTF4oZMK24eXz/rvtsEdTv9yJjcVQpdGx44GG4j7pxsTmlPBHac9b3Yk EJYlMnVeRYFz819W3kkCQ6dj2+8WU0jIDvq8vZDArQ8e8rRSCoIgyUvj0wQk T5e3eIgo5KoFBcKzBBLHTz6p/4NC1RqN9pyIgBNtplF6mYLmr5kXl64TqC+4 0vCkloKwwzj/0WMCW91H2rufUyipSIz7pZnA60woihUUKvhyr63PCPy29k4X u4vCbXPh1DM5gZExurK3m0Iv2yxO0UUgewd3uO81BfsBC6/+AQK/nxPrvx2h 4CZJZ1wcJBDhtNLo2igFjxylJmaYgJX41bx4FQVfe9GNt+8I5IUVW4x8pJAa z2KoVATskmtcVVoKmet+1tSMEziS/8PKmi8Uckz6O/lqAstC53lQMxTOV1ec mJz8+iv/tFk9i48LWbTYe1MEihIYvrdpfFwPiNmY+ZkA7Wxc4I/6fEhsmqzW TxMw9eratdqAj4ZxO83MDAFRfHS4Zi4f/wFrpDvO "]], LineBox[CompressedData[" 1:eJwVxXk01AkAB/CRqxy7KUSTMfy8pqRiY99K/L6xuqhNjtmm0wwG45zfsELE EvKqUWrQaposHUrHG+3qUNKSaAoliw6moajW0cRI2d0/Pu9jw43dEjqDRqNt /M//l6Zx9ZxC8j1Mf9km733S53GvnenLZkaQCZ3uPq5r6sjphtpfmcw9pDS9 ONFwTStZeuegtS4zj3w7lDTxzLuXjHJPiB63LiYTr0fN8vUeIds/hxcOW58j L4z2u5NeWtDv7mO9t64h67Jy/3BzM4HsgTR+yLqJ/LZDbT/TygZVl/K6o5Z1 kRZtZ4MOhDiBT7YWvxMqyZTuk0H7LVwRo1qslFe9Jc16sgOuGgIGNlmslz8M k+tcJhv+zPHCodnN9rLdY+Re+nK27tE14HYH3NZu+UQaJFNiRv16xP+VxY1l TZKNPxs9Tu3yxZU4I3+L9V/IAtOe1IKbP0GWIhh0ZNMQbaz3pSLOD5nSKb+P 77RwtFoww2NoC2jtr3AzWRvt07m9ocEBWCgKSwqw18Wefkm1bDIQr9WSIMNb euj1pvHWp7CxQRW590j8TKg7OweGGFux6bV4CYNhgFsSlsrlFgeD9dx99y8a YuFl5sug1duxzKTDymuXMQoNlY+HBnbAgFQH94x9g2MfJamnqF1Y+54zbhs4 G23z/J2bxLvReTdEi+NgAk2MRsoOCUZ17r2dTLUJjB1NU0ztuQjTTXilUMxB t0Ti1UrjgSdMqTYqmQu7pi2ukiYelvOXKHyDTXEjVdBffigEj+Y4GCa4moFV uSqyPCQUN6oyTzhom+P1+RdeOQ5hSNGy39zy3BzM/srqQF0+DHqS18XI56H/ TFFLYBcfqgqbQmmqBWoucT5Yy8JRuMhSpybQEnecd8a1JkVAXBLWGMycjy7h lNrTMxKcwh0Ko4H5yPjOraxVX4CJH8s10lo6eErbRd4vBFCqPJPu5izAp8Tu T1EVUTjt7kR/GGwFhVkM9qRH42J2ggl/KQMCpf8B5w0xyAnk+WirGUhLH6Br m8TCpUd2LuehNcTyI/7Vb2JRtPjExYc+TMyiW03rb41D+p2DRT41TIxala5g NcRhIz2w/IGdDSzNVkZscorH6pjGbSZ5NnA5kBex9lg8pAu4di1qG2ze5+x4 VUsIu/ozxzdts4We7GzZ+zAhxEvv2rfV2uLUm+anyx4IETam09pkT4CvpXrU 60KBe2WUmXeYgLJOPcEroRCV6T+1oYAA6yS/ye43Cgn+8mdGRwmIxo1LVKUU ctUJh8THCXD6xt34MgpVrprPklIC6j6PzMizFDR10x0VlQRGhvMt4q9RELcZ HbzXSMCg4JogrY1CSVl0+P4mAkvMSzzJJxTKRAqvdc0EDi+9bEnroHDNXDzZ rCCw/Rl1P+NvCj2cueHtTwnMSmQvyn5FgaW09OpTEqgdzBzJ/0DBUZ7M+F1F IE6a2+w7TGFldrcmdICA7uTtcuNRCr6s0stvBwlkhdVzDqspCAVMxsgIgbn7 6Y1HpiikrsrQXB0j0NZ24bT/VwrZxn1PRGoCQr/YNFOaCEWXyvInJghcOZ/z /XFtEU7v0+FfnyRQGP58DltXhEq/UM/UKQJdjJB/5umLILdtsPL4SmDFbXpL 50wRascWaqanCWx10zlXbCDCv2TLMnY= "]], LineBox[CompressedData[" 1:eJwVz3k4lAkAx/ERWutojUqImTEvWcfoejy04f0tHXKusDYdzDhD5JgyL9qI mBxps6JYUWzHg1WTUnJEpDIS1a7RJpMOsRuzsxnEtn98n8/fX2Ne7PbQRTQa zeNz/1t2iLd4bUiO4whjzH0RTRsd/Sx3f9Ze8lipmKOfpY2FzuYjLJaA7D9r krZlCR1lrXlMVZaQnBm/qyw11EG0A3/fR2YJqfTsUY3exmXon40o/MC8SGZH OdAMkvXwhWTEbILZSCpp6ejpHWGh4n553HtmN0lxc4cfLzNHbZ1QEm09SO74 YHYisMQG4WRfyXi8lPxL4nblYKkDYkbNpaLadyTzusG12vNOUDfOMHth94Es sZNU2fZtQb72A4uKIBlp7x3YNtHqCp7Et0X54b/kzXXrk2K0vRB3N4MXazZD lrs3oOiSN+r3a/robftE3q7f5B572QcVyVFja/xpSJAFBK8e9EN6+Zz3P+NK 6Hz/Ml806g9a/zCaKGUwbWfrPd7uwKrEsCRfC1XcuI57khW78Ep+6nuN24tR FO5o/ZK9B66jkak/xanB1LBtlycnCJ6vCiwZDHXcahnf47WJi7F23uF7NRrY 2vvpj1YXHqzpT42cA7UQxH1yMiE4GOqknDskWwINh+bdqVEh2DoR8JHtpw2f ntzsNmEofr8TohRgRce2JuF6WWUYrmV37GHJ6VDXjKF4F8MRpsofFot1YL2z zEG1MwLB8cnXNE8vxWAup0/Suxerwy3F7txlaBxOasoZiESvjpUGf8NylO6Y kkf9HYVbtelnrJR1MXXK0J7/MRrJShbfPXyui+mECaPa5TFQH6JcYkQroG7Z 4nXTOhaj1caF5Sl6UOGoWSca7Efh1/oqjX760Ao7RFVe2I+C02FdXJYBJgMH TYM4cQgo3C3WfGMAO9e3nhl1cZjeVKUob16J/omGtBb7eEhHnZLuZBlivjDO NLs1HpUOa1f2cI3AuOotCfdKQE0mnx7OYeBnnwWDgYEEZPkFuynLGdDc1rKx yj8RNkMVF7N6mHCms7l5o4koNj9T0+PGQurUGSktko8fW/OK3RpZOOp9LCVH wYfHSr+q+ybG8LYTR1FHD+DbmK6ddKExuo+r9Mq+PIhyQ57JQ7kx1vcs8cgo PgiT9l+LPHeyMXcgsu8XoyQUcO5YPG5m43p2l9jwbBLCZCp93RYEgm6sm6zn CMCrn2IJjxPw3Z6c/qhegOh0nznXEwTebqjkM0QC8H1EzzRPEgjIfxER3SBA tpyfX1BEQBRa5qV2S4DaDYrZU2UE0k1NGegQQNG28LT6MgHFpcCWuqcCFDzW zOvoIiBx8dc5PivA6XP7Io52E1gEqD3/JMC5RLGzywMC7a8d5y1oFBp0C2Ye iAm8t0wd61ShMBSwNKL/CYEi2Vz7vBYFM6m+84iUgGeiSnIMi8IaEcU4P0rg ydXN8U1sCt9kShShbwjs21q6V92UgrtZ2W/vxgjY+Ap/qDanEB/FYkxOEggO 49n+uY5Cin2a4oqMQOkFj9VWNhQytUYGEuUEpHRPM8qWQnHduZzpaQKbnfNX 6NpTqDysEn5zhoAtTfxViCOFy96hTilzBF73sNWugIKI3WnkOP/5pzqXRnOm 0CxbpVhYIOCUqaHw2EzhP9IZJTM= "]], LineBox[CompressedData[" 1:eJwVxXk01AkAB/CRM0elliJmfuNnTWGkXgeb/L5RKDrk2rRbjHHLlYn50UEk WVHZEk/jiLbnmLTSLSuNJEeRtdHWI8+6usbEoGZ3//i8D5sXtSdwHoPB2PGf /y88ylNbzc+0l42O6CoxCDR1EW4+RCi1O2wu5JU9AYWk/gRBCCnhqvevJUcI FDZksVSJDGryCkz/miUQsUlwcIp1iToiXqIyOM1G12xI7kfWNepCQdmr9C8k 1PsGOBOsO1Rzvc3BmwoOip+KYsZYLdTLzsrDJwlrVIsz+iKsXlG1/0y+rJuy QTD1/NJ47CBle+7ykyh1IHJo5WBt9QhFnD+U4uLrCE12KueNzUfKs2HcrdDc GWcWtZoX+0mpASOnK/T77eD1eT5UfvaFqsouWePH2YWYx6m8KM4MpRTNdWy7 7o6aaG2PZdu+UmHJM/PZYg8UJ4aPWvswMOTY083v90KKaM59clwJ9kk2rcSw Dxhdb3GfVkZmw9ENDiN7YRYXlOBprgpLnc25x5b9hHeyi95aD9RgWPNrrye5 H9uHwo6ci9HAUXGuSjzXDzvf5VgwmZow2fpIErHFH6OPeMefVGlh76hkuseF ByvdHmPHAzqoVgs0SA0IgCYl8++XLgDjhDP7dDgfzhO+UyZei1DJn3ZvzQhE byNfyddSF4GskZ6ZkiDcPNW0n5DpojI3ND/kWjCCVAVv29sXoyCizkhTEoKA 2MSb2vlL8KOOR8ubjlCsCrZod/P/Dgpval52dxg6FltqCWz1UOUzVhL5IRz3 qlMKLJX18eDDrfj4qQgkKpnvfvZaHw16+lNivUho9tMukbVL0RjL77tnFYWh cnauKGkZeiv8e+IMo5G7wkDljpcBTHpFGqW/RSMnP6jZnzBE0YZOkR83Br65 P7drDxtibaL37VRxDKa3lMlF9cuhetWs/6FdLAaHHBIa040g4pvGnWqIRcmm 1cvb/I0xvc2VFbLrEKrSBLrBXCYU+5O9u7sPId0rwFVZxkSFEye6zCcO6/qL r6W3sTAxIz2TNRSHvJUFVW2uBObur9BWChPgWENWnusdAr9kc4sy5QLsWO5V 9tSUDaXTbpn0ycPYHNm8TzeDDYnWijHp/HiIjHimz2RsaH1WD0rNi4fpo6sX du4zweXxjuHLxgnI4Taav6g3wZxCOmBUlIAgqcrzFnMSg5VQvsEVglfzmcjI JqFa1Hqus0aIiBSPue1nSXTYjqUxa4UQeNT+qX2eBH8LWxhRJ8QpmeBMzgUS D853HtC4J0S1rXz2YiEJi9iNVmgSQv6Hoqe8gsSeCbsOcY8QOS+0s5qaSdxy fszOnhUiv/RgyMkWEh9Dry59/VWI0rh2R5dWEjxKpGPBoFGnnzPT2k6iebxD LlGh0e+7JKTrJYlF19d2fdOhwRk0cBwYJFH+Qu10JEHDupZmXhkiYX94c/J9 Exo/pPXJA4dJBMacTdD8noYbp/D6yCiJ2z4xweUracSGE8xPn0gcd7J2+nsN jSS7ZPkNKQmhhp695ToaaToD3XEyEuOTC9bTG2jkiUszp6dJvFvvYKZvR6Pk uErw3RkSG5MTmXx7GhXugQ5JcyR+f9OifwM0ak0kxvbfSNx14y5kONKol5rJ FQoSTY1l6ju30vgXfpkvKg== "]], LineBox[CompressedData[" 1:eJwVx3k4lAkAx/EpVIvSpLXVaMx4p4wjsW2pFu8v9TwhFJKStjVy1SDHTMMg 76zzsTJbKkeTnK1HJlpdtlUmUU20YdMy+2QdeVLWOeuqZts/vs/n+bJ5kV5B C2k0mvvn/leWxFtkeyzL8Xr1tVEajYumDpabLyuMHObHJ9DsuNA0N/zAYsWR W3qPlBhGcCF7kG2iw8oktdniGIGKC76DIHzaJJ9spBX4WdWbo2M+NHfMpJIk hzmWZ+Mssbinz2zE5C6ZLx7xqPpiI4qfFkW9M3lCxpZM0BUOmyC/ntnDt+4m ZYmKPI6jPULIF/nvo/vJNzllm1wHnBAxaN5fJ39LovvPWsc3u6HLTjF7vXWM dKtyDmtPcceZ5UqL4u8nyS7/zp8vhHuC17P/vtazf0kbluTmwUP7EfUohRdp NkfKhOPPGfa+qD2p773K5SN56ffpafXoIRSLTwzb+NJg3eHS4tTrD0nRB8+p 9wswr6nRpl05ClpHL+7Fa4Gh0mXFmAdgfWywaL+FDm7FSlpvXOFhQH3xgN5v i3DnwRsJVxMI18HjiWejliBDFF7pJQ6Cx4DUksnUhexsTs3DsWAMP+QlP67W wxEPm9Fv3ENhTX+5dufRpVjZMTS7uyUMuqQ6QDW5DDrzEwku3BPYPeI3beqz HIavvKaGKvh4pTi2wM+KjuWPGyuuMiNwM6PpO5aaDmUKZ8uuxEgE6wh629pW QBlsLLqXcBKB0eKb+gWGWBNDH9hhHYWNIZZtbgErUeN+fn6fKgrPV1jpCbZ9 Cb3h+waW+dH4VS4ptNIyglwoPM13iYF4gcW+Z38ZYcmEWC5aEgtdVbxzRN1X mHKSCvWbYjFYwc4tSlgFd7knWydGgFzuau27PqsxNx5l/dhGCGlBcEsAaw20 7M7rj/4thF/ukTb9oTVoqF/lW5hzCjO7ymeLGhjw7ZB2091E6B90EinSjVHE vNIzPC9CiYMtozVgLSz60hln6uNQnSqgh2xg4uKmr7ef48cj3Sdwj5aaiThb RaUxQ4zNquLK9FYT3PPV2nvylRh55oXVrXtY4Czz0F6XmYDTD7Lz9txlAUGX 50udE+HO8Cl/ymHjx6m0gQrtJOyIaDlMz2RjUel6B926JBQZ8zjP1Gwc3tbf bRd9GpyHVy94HDbFSgdRWx89GdINCov2BlOUpFr7vwtNRvCk9osnFgTcEjUG h1qSwaudYGXmENiheF0sNKHAl3h/cP2JgOBalxGNTUHgXdelf47AfY+urExT ChlqwRnpBQL4ZURwaR0F+bbZ+YsyAv80Cl0VlhRmGzUvK6oI+HNnppZupSBt 189uaiGQ1F65t3wfhYLS8NC0JwTONec+svaiUBrbttNZSaDcNv3bO94UbhlJ 55RtBJTHJGbKAxRUfoahHX8QuLa4XTPmT8Gsf/XOvn4C9mmdtfZhFGzq4pll gwRMP27mNh+nsD21ZzZoiEC28vLlvXwKbmaymrfDBDghaVm8SArRJ1jM8fHP H1gdlCGgkGBPzd6YJKA66qKin6KQurSvM1ZNQFb23qtQRCHvemnWzAyBrE/O kIsplCRrh9TPEegzWHjbLpFClWeQU8IHArkBig2NSRTqTJvXOn4icHs8s8w1 mULD5PpZjYZAcMNBRidF4T9Q5i6T "]], LineBox[CompressedData[" 1:eJwVxX081HcAB/ArbA09HDKlzvGj85SdFXVyvp/UJtITSXEj57E6RO4ojz+R p4rKSiRJZc0rpWmb1mqe83QVUq+7K+aoTRniilS2/fF+vY2FkR7BsxkMht9/ /r84SfiZbVCO0+8Vz/0ZDC4autju3uw9pHyxb+ynhVzMNN09zGYfJNnZqn8Y 1lwU/3HMSIOdRSbCa/m6O7kQ8cXh74zOkk9OfpzIG1x0TYfljxpdJRYlBlJd oS0+l/dzho1qiDpTmHyp5WuUtpZEvTJqIZk6obNP3rDDRMEty96jLcRkoehF Qqsdvg1tU3ZOtRC2Rq9v7IAdXqu987rd1UryYouCzxnYYzV/s0NWRjtJ8agJ qqLt8fD6h9mckQfEM93+mdB7FZJbrd1s/buIrDDb012Phx+qfllW8X0X2bOm U/8LWx46C5zVzNq7iHNoa/bgJh5MQ3feMeB1k/jafUxGJg+tamk2DN3HxNRu flLHRx70+XKdB009RKX1l/uOUQdUXs+Si2xkZH2gf6RswhFDOkNH3QJkRJOr NSLU44MjcXMyz5eR5z8mndZdyccFR61S5ZSMyHr7BcMH+DjZcjTEp1FOBKJU J1rFh0SZO+YieEba/H4zmMMgKNFqO8z8po9YTP4q+LoACCWPzr6OVhJF9wq9 2jfOiBi0UFZX/k3uZwoS3/7lAk3jNE7v6lGSVrM7XJS+CccXtFmW7h4ns4Kk LpXh2yCUb7+n1v6W9EVqn9m9azuiGtOEkZz3JKoh+QXL0RtV+7U9DVw/EvEJ ReC7kV0ojd83xPVmQM/WNnpdnwCpJR+2TbyeBX+HHj/GBX8wuvpw55Aa0m4G 8g5YBGBZTEjcdksNVOjVy29eEGJAdWaH1u+fYbcgL8d8JhBug3sTT0bNQVPH j5Ue8cHYPJBnxWJpYn/6s5/qR0MwVC9MuX9NC/4jQWMrN4XBhtmzdJ3/XJSZ fTft0rwHmkQVoBifhwdabxNdzffBZdjnnYnXAvS1qateXhHhaV3QLB9rJlZb kPJyVgRuZTb4sVVMXPRMsV+fGIkQDXGfVKoD5UV+3J2E/QiMjr+lXaiL9l2W A2ttovBVqJXUPUAPRd/+ML1VEYUHOtZaYt5CdKyQzrc6G43fKlOLrNX0YZhN J4tcDyB+luXW9mf68IpMq4ybEwNNxaENEdVfokFxWqLdEIPBK8b5JQkGWD62 w1jjgBj55ovUa7wW4cKXEpv7XAnyCkOaA9iLYZdboD3ypwQ++d9JtV8uRnKM oXdRbiwm11+eKrlriCcap2RM9zgoB53j6jKWwHe4VD40HYeLfFvDjoCl6PPJ Mjx++yCupYuZoctZYItWOJwSHUKGV+BGNRULo/b1V5cYxsNOUXo1o8MIG7jq W/Y/jUeBRdG1jo1snGjYrG6WlYDkP44VbKxhI+rj+emyDYnYZOh1udXUGIdj MgauqCdhbUSzLzPLGC4LOHzN6iSULBGatquM0fi9UrYqOhmm9eWnN/ua4F5Q nLSfmYK85XWWnXdNoCy3EbwKS0HIuPqjFksKxYUz83c1p0BY9YadlUvhury3 VGJEQ5Tq+cHtBIWexif6DGMaYs/qJ9qnKMwLe5KTZUIjUyU+nneaQkT7sPic GY1K3tT0mWIKz2UStzorGlO1Mz1XKig8xOTE3NU08jq1jzU0U9AYurrl8lYa hWXhYUdaKGg+z2+08aBRFiNdt6GNwlzXjDW/etL4WT/vfZuUgn5CKqdtBw2F j25Y12MK91idM6MCGhzlonX9SgqKc91VjntocKsPsS4NUqjWtTdv2kvDIV0+ FfySArP//PktIhrunOIbfw9RyE08kiOMpBG9j80aG6PgdfBacKaYRoIjPXVz nAJD4qpgxtJIn9vfHaOi8PPt1x5FcTQKrpflTE5SyNRzRWU8jYsp6qG331N4 ZDb7l1WJNCq2BTsnfKAgjq1bXptEo9qkaanTJwpHP8++5JZC4+74sqmZGQpW 3TsNu2ka/wLxoqch "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotRange->{{0, 10}, {-15.999994285714433`, 560.2285677852391}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{{3.470311797530405*^9, 3.470311806158405*^9}, 3.470315064328637*^9, 3.4703723999647055`*^9, 3.472291942828514*^9, 3.4722941697569704`*^9, 3.4722942036093063`*^9, 3.472295405551547*^9, 3.4722954783438253`*^9, 3.4722975790372*^9, 3.4723005583719997`*^9, 3.4723007782852*^9, 3.4723013445808*^9, 3.472314165722787*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Energy", "[", RowBox[{"0", ",", "U"}], "]"}], ",", RowBox[{"{", RowBox[{"U", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{3.4723005258459997`*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwVk3k4lAkAh0WHRI8jOXIMn6MYYXdTKr4fow1hkytKzIWYj2VNhw6yCR2a YiWtFUlb1lHPZJdKdrKkoofBzIPUku1JqtEYDLXW/vE+73/vf68FK2kXV1VF RcV/gf9dcpy11Jlzxn1qqL3F6kyPe4uY5hdG20+KfzE87CG9Q863Nv1Iox0m Sf3nLEOpiCxpPme+hJZLHth5S6Im7SZ5bnxq2vwyqfPB4KJSMkyK5+IKZOY3 yaH7AUmTkk/ksoFh2/fmDeQ2q7EXExJVlD0pTX5n3k4qJRt/kkl0UVObO8Bb 30+KGDcqusoJxJJdl8dTRkjjlw3/sOgOSBxdNyKseUvq8qJuLWN8DQ2Lk7Yv N8nI887f3gsI2YQ87ad2ZdFysrfIqXlC2w2sgeCHas+myNMV6c9VjTyQ/NdJ VpLtLKlfMJKbX8LA7e81gwx9vpBZwT7u3VPbUHYkYcwpTAUprmVR7ZneyCz9 HDg5vgiMj7NpiSO+UBG/wv00NWRsDWQab/KHTWrMoWC7JXCtuSw8/vA7vFZc Cl3xYCkSZiYyHmsFwnc0/tjFZHXM2GsPOYTsQsBrgb2ZmQY2V/12tbAwCGOP WBmPq1dApusbHSoKxnqdPlNGlBaGz0aHpiwLhQapYA7KV8L740GfUZcwbH8f MW0Zoo0xtvoPwvTdkIo4iyLoOvCyMlDNFoXjbk7LPppCB9odNnl1HyMQs4T/ qrNTF0Y5tTtdXPaCnXLkrmaxHgrsXbX1YiPhGGvf6cdchVZjjw3yC/vwXJe+ gu+qDxcTkcCxLwr3ajKv0NVWQ1OtPJWZGY0ji+x2PnuxGiYnzLeG2zChMZjm nSg0gLr13vpdbUyMVloUlB41BN3NqPZgJAsFa40WN4QYIWlI95GvChuC4pg2 Js0Y4/KzIT5FbEQURHZqvjGGl2NrsY8DBzNe15WlTWvQKN8yN93Jwcio5yFR tgni6V/1d3G5KHdzXtPBNMXmD5ye8OUxqM7i68Q6mMHTytBfqzwG2SHsHWoK M1hnnD4k2hiLDYNlN7M7zLGW6/rQuj8WReuuVHfsoIHTFHdSmByH9OZzRTsa aGi62sOZ0N8P/zUh159YWWDy1/lpx9/3wyOxbY9OrgVY1lXLi/3jUWrCsnqm sMAHu3yXO7J4WD26URiwxxL1FXN/K3ISIHAQ2XU3WWK3F4EtZjzEyBd3tdsR MKKyG9Y388C6/YmWe56Angbvtn8YBV5m0GffCwTKGcfSZOEU+EFCiWY+Aadj eYz8vRRyFPw8QSEBP1ldr5RJocZVOXephEBWn0LJ5lFQ/jnfV1lFYKo83TPt BAVBt+a5ljYC0i354soqCsXXqLhT7Qsf8St+9qmhcC21k+H9lMBkzV3ueB2F +tWC2aedBHQspdPO9RQGI/TixL0EfNVNTR40U7AdMWIMjxBo7KnkiHspOAnT zCpGCXiv/MPhgJTC5qwBJfcNAcn29inDAQp+tiV1b8cIfGp8l7PvFYWUBJrZ xAQB+zKn6rdjFI5uPaG8I1/o9XscOPueQpbWcE+qYqG3Koh0lFEoqr12ZmaG ACeb35WqoFCesTi2cZaAvPlUscEMhapArufRzwQyZi+xG2cpCC1bTd3/JbDy m5v0yC8UmuQ2yvl5AiVUo2J+nsJ/7Y00bw== "]], LineBox[CompressedData[" 1:eJwVz3k4lAkAx3HjiGdGhzNHzIxXJpOrVrbsmveHbVONSkhLknGMMZiXpRWK dSR61GyR8Fgrm3SgY9RK2YqtRNMWaddRItGhZEwZKdv+8X0+f3/ZAsnmCHU1 NTXvL/1v+R7BnGXh+3kDc5weCt27ea2dLH4AS0TOP9Mz9n20jJy92ZzFYu0i 62kMsVl0K1l+rYCpxcojM+yqbDWju8gYt6TYD8wSctT9rY5K9Izs/BhVOM48 SZbxi5IVoklSu3eQM8ZsJN/7RJ0dF2mi8k5F/CtmG1nV5cN/KzJEXX1eb4xD D3n1cUjCH6sXQ0jeL3mdMERqa0/uulbqiLhh2yFZ3QtSRD80NdHvDDo7m/Nk 5Th5tsHlt+htrjiwoJ1buUNBjkznDWvtJiHo9ftTo+M9iYlERkuOB+L/yhZI ONNkzAAjg47VOEfp+pqs/URKzVNawtrXoDJV/NIpQA3Pa96k1ResQ2bFjM/k axq+ynLVmsv2hlrnAK6kaGBgS+yL+BMbYZMYmezH1UIIr7MyfLkPnimLtzCu zkHbT0EuJbs2Y91w9O5D8Trg9zzXWtPniw3PpEstLelIb4zISl7pj5ctgozb tQw4kJtGl+/eAge9bgvPkLlQjrnti+wPAJ1UhvYp5mGlZ/F8wuYHrBkL/GDl vwCHryvub80PxD83wmmBdnqouOLpoT8ahIZ9rdtZSj3YbJ8t8XMIRqRW0oBc ro+bS5rtFki3IywhtUG31ABPS0ar/XpC4ChcKueHGqLbM0s47+AO3NO3YySt MoLXPQPTel4omuoyy+w0jDFlH8grHAxFKo27qaPfGM5sK5pLoQD0vhSvONlC 3H4wVFriEYbhanZhRZoJSgOCatyHw1C4xFSz0d8UU5Sfb3VROKSlkbdCWWYo CtZI2OgagcDCYLnuiBnydM4IL/dGYOq746qKZnPQvbqnn+ZHYmjYI/lG7iLc DrxI2+AgxDG3ZeZ3Qy1gqG5SvfOJELU5SXpCe0uUpzk2D2VHIdc/bL2G0hJ7 GlCrzxFhRV/lydy7TLzK7Fz1uVuEo7ZltXfXs1BMLHJ1SI1G+rWCo+sbWZBv ff7IzF4Mb3P/43es2Qjmn+K39YrhHncrSC+PDa6B9Yore2JQsUhg3aFkIzOO 2SR2jIV1y4kjG4KsYFb+tyykKxZS+xvcB81WoOen5hjtjEOkQvN+G5fAXkaN InexBIJzE6y8gwTIHfkPeW0SxGT6zqz7hcD4Be0e0w4Jknxlj3QPE/hVO+fx pFyCfcqkA9IjBD7VpY+c6pKgbpXqY3E5gaZPiSrjAQlU12e7q08TWFEWYvH2 vQTSB7oFrbcIGIlLz2/Up1BaFRu1t43AmOG/zlcNKFQlyj292gm0Ni+8xDWi cNFYOt0uJ5CoX9SkZUKhL9AgqvMhgc7Gg61NFhQ4Q6aeg0MEpDo53RxbCk6y FMvfhwkIz7dsLeJScM3pVUWMfPnZpt6rbkeBzyk/++IlgTf16U/6HSgkiFmW 794R8A5IGT3sTCHt259V5xUEFtMao2kuFHLmDnYlKgnMnPrwOu5rCkfrq/ZP TRE48znx3VpXCscyNIWXpwlk11z48dI3FE77RHikzRAI2jyhtHajILO6acH7 TGD5jFPyIR6FZoWNanaWAL1aMj1LUvgPRCsrqQ== "]], LineBox[CompressedData[" 1:eJwVz3k4lAkAx3HjiGdGhzNHzIxXJpOrVrbsmveHbVONSkhLknGMMZiXpRWK dSR61GyR8Fgrm3SgY9RK2YqtRNMWaddRItGhZEwZKdv+8X0+f3/ZAsnmCHU1 NTXvL/1v+R7BnGXh+3kDc5weCt27ea2dLH4AS0TOP9Mz9n20jJy92ZzFYu0i 62kMsVl0K1l+rYCpxcojM+yqbDWju8gYt6TYD8wSctT9rY5K9Izs/BhVOM48 SZbxi5IVoklSu3eQM8ZsJN/7RJ0dF2mi8k5F/CtmG1nV5cN/KzJEXX1eb4xD D3n1cUjCH6sXQ0jeL3mdMERqa0/uulbqiLhh2yFZ3QtSRD80NdHvDDo7m/Nk 5Th5tsHlt+htrjiwoJ1buUNBjkznDWvtJiHo9ftTo+M9iYlERkuOB+L/yhZI ONNkzAAjg47VOEfp+pqs/URKzVNawtrXoDJV/NIpQA3Pa96k1ResQ2bFjM/k axq+ynLVmsv2hlrnAK6kaGBgS+yL+BMbYZMYmezH1UIIr7MyfLkPnimLtzCu zkHbT0EuJbs2Y91w9O5D8Trg9zzXWtPniw3PpEstLelIb4zISl7pj5ctgozb tQw4kJtGl+/eAge9bgvPkLlQjrnti+wPAJ1UhvYp5mGlZ/F8wuYHrBkL/GDl vwCHryvub80PxD83wmmBdnqouOLpoT8ahIZ9rdtZSj3YbJ8t8XMIRqRW0oBc ro+bS5rtFki3IywhtUG31ABPS0ar/XpC4ChcKueHGqLbM0s47+AO3NO3YySt MoLXPQPTel4omuoyy+w0jDFlH8grHAxFKo27qaPfGM5sK5pLoQD0vhSvONlC 3H4wVFriEYbhanZhRZoJSgOCatyHw1C4xFSz0d8UU5Sfb3VROKSlkbdCWWYo CtZI2OgagcDCYLnuiBnydM4IL/dGYOq746qKZnPQvbqnn+ZHYmjYI/lG7iLc DrxI2+AgxDG3ZeZ3Qy1gqG5SvfOJELU5SXpCe0uUpzk2D2VHIdc/bL2G0hJ7 GlCrzxFhRV/lydy7TLzK7Fz1uVuEo7ZltXfXs1BMLHJ1SI1G+rWCo+sbWZBv ff7IzF4Mb3P/43es2Qjmn+K39YrhHncrSC+PDa6B9Yore2JQsUhg3aFkIzOO 2SR2jIV1y4kjG4KsYFb+tyykKxZS+xvcB81WoOen5hjtjEOkQvN+G5fAXkaN InexBIJzE6y8gwTIHfkPeW0SxGT6zqz7hcD4Be0e0w4Jknxlj3QPE/hVO+fx pFyCfcqkA9IjBD7VpY+c6pKgbpXqY3E5gaZPiSrjAQlU12e7q08TWFEWYvH2 vQTSB7oFrbcIGIlLz2/Up1BaFRu1t43AmOG/zlcNKFQlyj292gm0Ni+8xDWi cNFYOt0uJ5CoX9SkZUKhL9AgqvMhgc7Gg61NFhQ4Q6aeg0MEpDo53RxbCk6y FMvfhwkIz7dsLeJScM3pVUWMfPnZpt6rbkeBzyk/++IlgTf16U/6HSgkiFmW 794R8A5IGT3sTCHt259V5xUEFtMao2kuFHLmDnYlKgnMnPrwOu5rCkfrq/ZP TRE48znx3VpXCscyNIWXpwlk11z48dI3FE77RHikzRAI2jyhtHajILO6acH7 TGD5jFPyIR6FZoWNanaWAL1aMj1LUvgPRCsrqQ== "]], LineBox[CompressedData[" 1:eJwtxX1M1HUcB/AjQA3O5qmRiNz9ji/z9ETTtbZoyfedtFKeJuKpO6Z5B9wh Dwd3X24zoDKSkDn0UqYIYzfEhzkHPux0w4oUSULgmlL2cLQc581BumnXJYcU 1X6fP157ac0VW4peUCgU2f/5//aPzHPWFR5Mk/el9Y9KWdulPVy+h8/e6v1U kj6gB3n79SZNtNRI/8zL1jvLn2lO0BN89Hlx8xPNOTrM5/rGdY81PfSL6Ljt tv+uGeTy8ei+0OgrW/MLl9fDyu+ceOTwc/nXYAus9Hu6J7h8KmK0+3W/vfGE ywOHFgzpO3YHuXw6zL6tX0cO/8Xl34X9m/3mCt00l8/ApUpl3pJNf3P5bHTU lE6u3a6gN6POPZP756MIOheK0fv4sjqSzsPyKsverfpo2oAHoePbYr+aQ29D RqDkwyP2efQO5DxwrVKrY2gjJm+a933bFUvnY43qXmL6+/PpnYjhIdNY8CV6 F957bHyWZFhA78ZPfYURxhQVbcKVA/27pJCKNsES7bzv9S6kzShw1FxRti6i C/CqdZU3y7SYLsR3C1Ninakv00X4oruuLSUyjragJkK/efjXONqCmLHqjTbP K7QVgTPaZnftEroYzSvio3oM8fQeuFotAyZpKV0CY/NOr/LhUroEU++cDrt7 E+hS+AMb9vY1LKPLcHL9uoQRUyJdjq56p8q6Wk3b0GAoyIwMqWkbXh/rONcw oqEr0LKyrWskU6Ir8fH1ppbMHomuRHaC4fTtZC1tx9u2gXxVo5a2w73MnDwc 0tJ2JN88eywnP4l2wLW6T3+3N4l2wBKMujOoZ7SA+dIfUuNhRguU1eXNZHzO aAFnnudH5VFGCxwIOQ+5jjFaoDs1/Px4O6MFwjdm7505z2gB111lU/8AowVa O8uLPxtktEBnlTd94xCjBa7GuaaHvIwWGDMuKh79gdECOn98+rif0QJrPdXq UwFGC7xZ7wsXPWS0QJau/eLEJKMFHKWS+ulTRgvUvvVJ+HKQ0QL188e/rwox WqDlQufBqSlGC5zcF2W9Ns1ogfO5RRtqZxgt4Em6lZj2D6MFeoPLw7OzjBb4 F0LMOOM= "]], LineBox[CompressedData[" 1:eJwtxX1M1HUcB/AjQA3O5qmRiNz9ji/z9ETTtbZoyfedtFKeJuKpO6Z5B9wh Dwd3X24zoDKSkDn0UqYIYzfEhzkHPux0w4oUSULgmlL2cLQc581BumnXJYcU 1X6fP157ac0VW4peUCgU2f/5//aPzHPWFR5Mk/el9Y9KWdulPVy+h8/e6v1U kj6gB3n79SZNtNRI/8zL1jvLn2lO0BN89Hlx8xPNOTrM5/rGdY81PfSL6Ljt tv+uGeTy8ei+0OgrW/MLl9fDyu+ceOTwc/nXYAus9Hu6J7h8KmK0+3W/vfGE ywOHFgzpO3YHuXw6zL6tX0cO/8Xl34X9m/3mCt00l8/ApUpl3pJNf3P5bHTU lE6u3a6gN6POPZP756MIOheK0fv4sjqSzsPyKsverfpo2oAHoePbYr+aQ29D RqDkwyP2efQO5DxwrVKrY2gjJm+a933bFUvnY43qXmL6+/PpnYjhIdNY8CV6 F957bHyWZFhA78ZPfYURxhQVbcKVA/27pJCKNsES7bzv9S6kzShw1FxRti6i C/CqdZU3y7SYLsR3C1Ninakv00X4oruuLSUyjragJkK/efjXONqCmLHqjTbP K7QVgTPaZnftEroYzSvio3oM8fQeuFotAyZpKV0CY/NOr/LhUroEU++cDrt7 E+hS+AMb9vY1LKPLcHL9uoQRUyJdjq56p8q6Wk3b0GAoyIwMqWkbXh/rONcw oqEr0LKyrWskU6Ir8fH1ppbMHomuRHaC4fTtZC1tx9u2gXxVo5a2w73MnDwc 0tJ2JN88eywnP4l2wLW6T3+3N4l2wBKMujOoZ7SA+dIfUuNhRguU1eXNZHzO aAFnnudH5VFGCxwIOQ+5jjFaoDs1/Px4O6MFwjdm7505z2gB111lU/8AowVa O8uLPxtktEBnlTd94xCjBa7GuaaHvIwWGDMuKh79gdECOn98+rif0QJrPdXq UwFGC7xZ7wsXPWS0QJau/eLEJKMFHKWS+ulTRgvUvvVJ+HKQ0QL188e/rwox WqDlQufBqSlGC5zcF2W9Ns1ogfO5RRtqZxgt4Em6lZj2D6MFeoPLw7OzjBb4 F0LMOOM= "]], LineBox[CompressedData[" 1:eJwVxX041AcAB/CzK/VwbZG3wr34KbkQ9ZS05feNraGXKckzZnKHIxwuF7+f U6a8lnbMk7dHkuLpaZTm1qiwUipcifB0VN5qpZ7RdXGnddv++DwfniBhT+Rn DAZj53/+v/KwwNAt4rinZY2rU7t21LOjj7sjiBtDavM1vh7p7aT+TutRLpci S9ZJ95mnPyQr2ws4C7l5pMhQ8QMz/TkZt0UaP8spI7+b7g/TyabJvvno4mnO BdJrMmJUI2NgkWrM4S2nmbzxzOmsWrYU1ferkqY490jdsDzznYyLhkt5qjiX J6RfiGliiosbRGRv2RvJOOleM5Y3kO0B8aTjeFPDK1J+eJmi9glgxDvm8GzT NBkaOzJ+zu8bnFzaxa/eryZbsvi5fWJfCFR725jdH8iZMM5Ux9ROJN0+Jkhw 0JFFvDqrUcfdaExkBVj5/kO+d8z4MOsegOq02NeuQQx4m9avT5QEIrPq4+73 bwwQUlhxkZETBEbfc1ynmZg2czC3LPweq5KjUvfyF0KSavj0ZGcIJjQl+4xv GOKapG6UPRQKv8kD6UVJi0Gt2mWXa7Qfuybka9hsI/SZl3TfIsLx+pYg4269 MYoeotiYL4CLyYCtd9gSbEsrNj62TQgjUhM+rP4cYTM+Zxb7R+Dbt8GzdoFL ER9UN3EjIRJDNyMMgp1McJ3s523Mj4Iit+NHrsYEYnW4rKVQhKiF0udKpSks SsqyEy5FQyhJU7DKl8HOcF2Da0sM1orWKHeEm0E8W6psajuAB6ZOxlIPc1we unA6RhWLaw2ZFU5MCwRmWZ/gT8QhzYDv3z1igRmeu6MNUwyjYdpH3GSJHvDa HtokYLKWV1wls0K2+cbmuyaJKF69fEFz4HJUZ14+sPVMIuTlUZ3h3BUQB6r4 WJmE4OJQJevlCoTExIvO1CVh7uvz2qpWa3hL++etNkgwPumVejPHBiMvpk5b NktwdoubdU+4LST+Q2UuPgdRnyU1ETmz0cKR1nT1HEROoHA7U8MGz5VyvO+f jA3D1Rdyejg4umnPotGnySh1rKjv2c5Faa1KnS6U4kh7Qen2Zi7qWJs3rVdL sdM68Px9ex4e/6af8804hK3izhCTPB4U7dK7L5gpqLIR2HdreCi83f53RVEK 7G/VndoVYgeO6/WVg5apkDvf5D9qtUOPij10sDwVUeoFvff4BA4d2Te2ejUF QeM7bt7PBHpzPeeFv1KIywz46FdIwKXCOfZKAwVpQNMg6xcC+fU2KkYjhVyN 9KT8FAGvR7qWSgWFBg/tfEklgSbrq/RgKwXtn/qB2osEShrW6vx6KcgfsQo6 OgmE9nO1bh8olNfER2ffI9Dy4ouYjDkKNclKb58uAhbaT0NKHYXfLeS6LiWB B7Yjf8TqKQwHL4vue0xgq6gs9fxiGg7jy73HxgkQOpM5K2sark00+9wkgSMs g2iRLY3NWSpt5EsCw+zpQQWHxg6HysuvXhMo9lZe3WNPQxLLZc/MEDAsyE85 4UxD9tVP2itqAsIq6uWTtTSyloz1J2sItDVGBzmuo1F6qeb43ByB1IFt7nc2 0jibsUDUoiPw+K8NdWYeNC7ujvSSfSTgOm9vKfySRpPdHVvPTwROLDHLadxC o1W9SqvXE3jFYc7qSRr/AtQjM7A= "]], LineBox[CompressedData[" 1:eJwVxX041AcAB/CzK/VwbZG3wr34KbkQ9ZS05feNraGXKckzZnKHIxwuF7+f U6a8lnbMk7dHkuLpaZTm1qiwUipcifB0VN5qpZ7RdXGnddv++DwfniBhT+Rn DAZj53/+v/KwwNAt4rinZY2rU7t21LOjj7sjiBtDavM1vh7p7aT+TutRLpci S9ZJ95mnPyQr2ws4C7l5pMhQ8QMz/TkZt0UaP8spI7+b7g/TyabJvvno4mnO BdJrMmJUI2NgkWrM4S2nmbzxzOmsWrYU1ferkqY490jdsDzznYyLhkt5qjiX J6RfiGliiosbRGRv2RvJOOleM5Y3kO0B8aTjeFPDK1J+eJmi9glgxDvm8GzT NBkaOzJ+zu8bnFzaxa/eryZbsvi5fWJfCFR725jdH8iZMM5Ux9ROJN0+Jkhw 0JFFvDqrUcfdaExkBVj5/kO+d8z4MOsegOq02NeuQQx4m9avT5QEIrPq4+73 bwwQUlhxkZETBEbfc1ynmZg2czC3LPweq5KjUvfyF0KSavj0ZGcIJjQl+4xv GOKapG6UPRQKv8kD6UVJi0Gt2mWXa7Qfuybka9hsI/SZl3TfIsLx+pYg4269 MYoeotiYL4CLyYCtd9gSbEsrNj62TQgjUhM+rP4cYTM+Zxb7R+Dbt8GzdoFL ER9UN3EjIRJDNyMMgp1McJ3s523Mj4Iit+NHrsYEYnW4rKVQhKiF0udKpSks SsqyEy5FQyhJU7DKl8HOcF2Da0sM1orWKHeEm0E8W6psajuAB6ZOxlIPc1we unA6RhWLaw2ZFU5MCwRmWZ/gT8QhzYDv3z1igRmeu6MNUwyjYdpH3GSJHvDa HtokYLKWV1wls0K2+cbmuyaJKF69fEFz4HJUZ14+sPVMIuTlUZ3h3BUQB6r4 WJmE4OJQJevlCoTExIvO1CVh7uvz2qpWa3hL++etNkgwPumVejPHBiMvpk5b NktwdoubdU+4LST+Q2UuPgdRnyU1ETmz0cKR1nT1HEROoHA7U8MGz5VyvO+f jA3D1Rdyejg4umnPotGnySh1rKjv2c5Faa1KnS6U4kh7Qen2Zi7qWJs3rVdL sdM68Px9ex4e/6af8804hK3izhCTPB4U7dK7L5gpqLIR2HdreCi83f53RVEK 7G/VndoVYgeO6/WVg5apkDvf5D9qtUOPij10sDwVUeoFvff4BA4d2Te2ejUF QeM7bt7PBHpzPeeFv1KIywz46FdIwKXCOfZKAwVpQNMg6xcC+fU2KkYjhVyN 9KT8FAGvR7qWSgWFBg/tfEklgSbrq/RgKwXtn/qB2osEShrW6vx6KcgfsQo6 OgmE9nO1bh8olNfER2ffI9Dy4ouYjDkKNclKb58uAhbaT0NKHYXfLeS6LiWB B7Yjf8TqKQwHL4vue0xgq6gs9fxiGg7jy73HxgkQOpM5K2sark00+9wkgSMs g2iRLY3NWSpt5EsCw+zpQQWHxg6HysuvXhMo9lZe3WNPQxLLZc/MEDAsyE85 4UxD9tVP2itqAsIq6uWTtTSyloz1J2sItDVGBzmuo1F6qeb43ByB1IFt7nc2 0jibsUDUoiPw+K8NdWYeNC7ujvSSfSTgOm9vKfySRpPdHVvPTwROLDHLadxC o1W9SqvXE3jFYc7qSRr/AtQjM7A= "]], LineBox[CompressedData[" 1:eJwVxX041AcAB3ByzLwslJeSu+OnLi+9PU/zxOT37WV6U8ucmlPicOgQcuLu 4n5KuTVSCXl5dDWsPGk19cTGhNg56clbW4zCzZJSdLiXZtsfn+fjyD32deQi PT29vf/5/7J0rtGGiHM+8rUFyptz4z6tPUy/g8wY0q+ulOune0QutDWeYjLT SMZb3+MrdH1kWVMOw5ApJaXGpSKaTknGbhbEzTGukI2X2zLmtSqyRxud/45x gwwaHKCmtYb4ZGCE9YZRR1Zm/JU5pbWGrKM88TVDTu59yjd4q12JmtvSgdi1 z8kHaXYo/9sDUeTTK5NJo6TQttDoPG0L4pUuo7U1r8imH1p9h1J9YeJ4mjW8 6R3Z7cnKOhPuh1wLhassdIYU1yQa5nzYD+4A+1eDzllyljy649R0ABIfneYe Y2nIFveNKdTIAdxJMAuw2/WRLBm5uVNVHgSZiD+x/qAeOHbexZeLDiGzXOf/ YVIfzrbC89UhR6DX8wK/CA1w9UHrgwjTMKxK5qWyXQ0hqwh69WkWF2OqwgOm DUZYPdf6OkYZjt3KoycvJhpDlt2wJjQ8EvvG8tzodBO0ttN5nOc8TLRwJb/d MkUc/0DC4k3RWGvZ77DtiDmMv7Kv5/wUAxNSFTY48xlcCu/3hVrzseMNZ84p 0ALejOH1H/Nj8XtzhD7H3RIadkJmmXk87mW3hjBVltg89axiPvYYeIaCF11d VqiL4NFUyQkITxLdMyteAltaJ12xKhHroty6/MKWYpcmciPRl4gnVu6mAk9r CPLaYnwvJuHnmswSdwMbjH1jZdy+9ThE+q77O/+0gd9D5zarRckwGRTujK+1 hVTCz3jRkAxlpWN+udgOxkllMtM4AfJXL6PVBS5DpkHBqL5bCvKKee1hzOXw aU/LDRxMASf/cJfZ+HI8eXlho9u3JzC/vUJd3miPoNIEjcI3FaPKranNZ1eA JfVy6ZhNxbXNG+wfhzngrbXixKV7abiVJbCMWkPHXK/vuvooIc4Ghu8xUNHR PzH7kmsjwueDshtnHzNQczWutr9HhCKXkluP9zDRkf1kquq0GBlNOUV76pgY spjfvX37Sey1D6zocHZE+xRbxtVLx5b49mBLqSOm9cpCh26no3wF17lT5Qib u9XkyvgMOLdUFewLdkJTR3fL2GIJ8tY0u3Y3OmFoPEY5x5OAN0N7KncloGaP FSQ8koB7Z5opPU/AI7hXV+hAITYzQLf7AgG6lbzUkUFBEFD7zOwSASN5g3c1 k0K2SpCbV0DgmUeVuJGgUOOp1haWEUi1EurGXCioHy70V1YTqJczdBs8KOR1 m+W0thPw2cTXKvZRKL4eF31GToA1daQkcD+F68ld23YqCCyuZH8x7E/hvk2e RtFFYHiJj2iaTWGQsyS6p4+AZMpCaxdMgTW6bNvIKIHmyvuayCgK62uF9O+V BG4eri6eiqbglTWgjhwncGnpVa+0oxT8WGU/vpogwM2UCr+Lo5DEZ9LfvydA CzmkuXucgtibUt+dITC51L/YW0Ahy3ykN1lFoFfxpVdbCoWi29fPzc8TqPBc J/wjjcI1CS2qXkMg9x2xPFxEodo/cqtYRyClyq5+Ukyh1qnNwecfAiEh5pyU dAqNM6vUCwsEfK0XaRYyKPwLpaY63w== "]], LineBox[CompressedData[" 1:eJwVxX041AcAB3ByzLwslJeSu+OnLi+9PU/zxOT37WV6U8ucmlPicOgQcuLu 4n5KuTVSCXl5dDWsPGk19cTGhNg56clbW4zCzZJSdLiXZtsfn+fjyD32deQi PT29vf/5/7J0rtGGiHM+8rUFyptz4z6tPUy/g8wY0q+ulOune0QutDWeYjLT SMZb3+MrdH1kWVMOw5ApJaXGpSKaTknGbhbEzTGukI2X2zLmtSqyRxud/45x gwwaHKCmtYb4ZGCE9YZRR1Zm/JU5pbWGrKM88TVDTu59yjd4q12JmtvSgdi1 z8kHaXYo/9sDUeTTK5NJo6TQttDoPG0L4pUuo7U1r8imH1p9h1J9YeJ4mjW8 6R3Z7cnKOhPuh1wLhassdIYU1yQa5nzYD+4A+1eDzllyljy649R0ABIfneYe Y2nIFveNKdTIAdxJMAuw2/WRLBm5uVNVHgSZiD+x/qAeOHbexZeLDiGzXOf/ YVIfzrbC89UhR6DX8wK/CA1w9UHrgwjTMKxK5qWyXQ0hqwh69WkWF2OqwgOm DUZYPdf6OkYZjt3KoycvJhpDlt2wJjQ8EvvG8tzodBO0ttN5nOc8TLRwJb/d MkUc/0DC4k3RWGvZ77DtiDmMv7Kv5/wUAxNSFTY48xlcCu/3hVrzseMNZ84p 0ALejOH1H/Nj8XtzhD7H3RIadkJmmXk87mW3hjBVltg89axiPvYYeIaCF11d VqiL4NFUyQkITxLdMyteAltaJ12xKhHroty6/MKWYpcmciPRl4gnVu6mAk9r CPLaYnwvJuHnmswSdwMbjH1jZdy+9ThE+q77O/+0gd9D5zarRckwGRTujK+1 hVTCz3jRkAxlpWN+udgOxkllMtM4AfJXL6PVBS5DpkHBqL5bCvKKee1hzOXw aU/LDRxMASf/cJfZ+HI8eXlho9u3JzC/vUJd3miPoNIEjcI3FaPKranNZ1eA JfVy6ZhNxbXNG+wfhzngrbXixKV7abiVJbCMWkPHXK/vuvooIc4Ghu8xUNHR PzH7kmsjwueDshtnHzNQczWutr9HhCKXkluP9zDRkf1kquq0GBlNOUV76pgY spjfvX37Sey1D6zocHZE+xRbxtVLx5b49mBLqSOm9cpCh26no3wF17lT5Qib u9XkyvgMOLdUFewLdkJTR3fL2GIJ8tY0u3Y3OmFoPEY5x5OAN0N7KncloGaP FSQ8koB7Z5opPU/AI7hXV+hAITYzQLf7AgG6lbzUkUFBEFD7zOwSASN5g3c1 k0K2SpCbV0DgmUeVuJGgUOOp1haWEUi1EurGXCioHy70V1YTqJczdBs8KOR1 m+W0thPw2cTXKvZRKL4eF31GToA1daQkcD+F68ld23YqCCyuZH8x7E/hvk2e RtFFYHiJj2iaTWGQsyS6p4+AZMpCaxdMgTW6bNvIKIHmyvuayCgK62uF9O+V BG4eri6eiqbglTWgjhwncGnpVa+0oxT8WGU/vpogwM2UCr+Lo5DEZ9LfvydA CzmkuXucgtibUt+dITC51L/YW0Ahy3ykN1lFoFfxpVdbCoWi29fPzc8TqPBc J/wjjcI1CS2qXkMg9x2xPFxEodo/cqtYRyClyq5+Ukyh1qnNwecfAiEh5pyU dAqNM6vUCwsEfK0XaRYyKPwLpaY63w== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotRange->{{0, 10}, {0., 559.9999885714285}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.4723005277492*^9, 3.472300566094*^9, 3.4723013453296003`*^9, 3.4723141658668303`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Energy", "[", RowBox[{"0", ",", "1"}], "]"}]], "Input", CellChangeTimes->{{3.47229508185118*^9, 3.472295124301425*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "24.`", ",", "26.`", ",", "26.`", ",", "32.`", ",", "32.`", ",", "42.`", ",", "42.`", ",", "56.`", ",", "56.`"}], "}"}]], "Output", CellChangeTimes->{{3.4722950830933046`*^9, 3.472295124917486*^9}, 3.472295405668559*^9, 3.472295478407832*^9, 3.4722975791152*^9, 3.4723013453608*^9, 3.472314165879834*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Energy", "[", RowBox[{"1", ",", "U"}], "]"}], ",", RowBox[{"{", RowBox[{"U", ",", "0", ",", "2"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470311825776405*^9, 3.470311897139405*^9}, 3.472291982631514*^9, 3.4722951743764315`*^9, 3.4723008960495996`*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwVkHk41HkcgB3TRkJ02FFMI9pIEhKhzwfzixWKlCNhlSNlS42iDU07hGjs rtSGVHSIHDmyUaZIS0quRcso5tEUOYpxDd9t/3if99/3eZn+R10DZKSkpJy+ 8b8dAkTN/I8B2wx6nEoIYfBpturHeuks6Hw4ujhkmME3zrqSUUJ3g2GmVl17 N4O/41XHg0z6Qfj6Inpn8V8MvvvByce/09nQlsFMiDjB4PdsPG+bTOdCM7de Qn3Q5F9fvjMukZ4Kag5j9W+aNPgcuZIfEug54OUqyd2Zs5Lv4XmjcHSsFOjB T+T7JSv4CoTjbadZDcNpy/cZFqvydVyGRTUXamF+kLfnrZwi/9Rrc7gyXg/f mbQ2qyvQ+GqlKgJp6SY4aeAhcgyerC7vs21ssmwBcUIDy6O0vfpZSOZKz6E2 4EXmcsIdRDCx1kr5fmgHxLGNg6YjJCAznbdkpc5biMs53S5QWoimxK98d0E3 CAZVjxeylLGRa/K6Tq8X3CqK/v3n1lJkpAxO5w6/A4b5AivRnBoOTvYK2g37 ICHUMXCT/CrM+VTZoHSxH9YE1zvHmaxGJY07I0KhEMJ9JnI0PbUw6VBZ4HXt AaAlGHV1uGujGPOEwTEfQFbw9I+es2uRbVRbuqJGBA/mXxoBdx32FtReaGZ+ gr32dLqwWA9nQ9rSdU8Pgn34xazMNn1cb71wPrByCMKydj2XbTFAu5vMoGK1 Ydi+2Gx16xlDPKXhq/XeewR+Y4THKEZvQv2hPQodTqMw7fXeaCrSCJcqj8rV zoxCY1LfXkmiMdKq0wvXZIzBhKvpNm6CCR42qeyS3/EFXkTIjDAyN2Pej/7X n4i/QHt0uRM7zxQnBtWXDKR9BS+x7iP/O1uwbLedbCprHAyU7sX4VphhjH1s VunAOLztb1wn/dAcmT0OndmxE+D9cIlzWNFW3LqFm0o3EkOjb/neT08s0Fuz aVq6VQxJ+eyS7ystcaIhue8YZxLqputrHRqt8ArNh+2qPQXu5pq8rS+34VJB 2U2Z2imIkBOyac8BF0Rx3MzDpmHPbLLfwCFEqVyfwj7VGUibsfi6UYR4/Gph suqzGdj1U6er+Jg1Pl4fL6fy8yykX7Lr1Ju0RhWH4/rnlCSQ7ZFY7sC2we4N b1ojqyRQYenVJJy1waJroC30mQN3/Uqz0NO2uL/QVEVjfg4inmZVHRLb4tnY G5zue/PAg6vygjMsvC/SSFdyJBBVpfwLNcPC+MxYP4EzgQ8PupzDJSw86PpZ p8CFgFdKPPPWPAtXVVUVObkTuHvqUg1NlsJE3r66JH8CGuZHZ2oUKAw2/XNs USQB6yhLYxsNCrW4y+wX3ibw65HFLVZI4bzZGcWOuwT0efnnQm0o7Prc33I7 j0DD9s1GmSwKU9xL9m8vJqD4UeqixJ5Coud6IraKANHmmlW6UNjdzLsm20qg 5uluT7MDFFbETR5obScQ+CxxKiiAwlQLX93szm99Ovlpl4Mo3HHLoNRGQCAn rqBJfJjCRxGv6jkfCWi3lpqUsSlM27CZ5zJEIF/e5qXwJIVhfRluzBECAecf +S2LpHCd45Fe/jgB3YbQ+BNRFNKk23JSJgks+/uuenYMhe/KLEL8Zr79im7K a+FQWBWSvdFwjsDcoj4LGS6FlxkKE4QQyI1/17ApjsL/APBkX4U= "]], LineBox[CompressedData[" 1:eJwVzms01HkYwHHXKFJUNGmIJUkkUUI9T0Zm/nRhKLWRySXShdRGmw0dtxQ5 jiMVNagUh1Eua8OasNqsRJRLYxRT5K6dMS7x2/bF93zefvV8gtn+cjIyMvt+ 9L9O/oOt/K/+u5Ld9biEaPEVGGtCemkOcHqgBxWHtPhb72dkltDcQcNJbXZp uxbf+XXHsyyaH7AijPM3PNbie/hJq1NpF4CbEFd81UWL37M5npFEi4FzjUe7 GrI1+dxVB+ISaWmQK7JyiXBcxY9WLjG6RnsA3Qpe75dkaPAPH8nmTUyWwreL H7acaFnMVyHRnkydGhA6jbWMDy7UGLqODdZdr4fU+DwX6fznmrDmHZAhfgWC v+Yl4nARaJWqC2Vl38CAvyrduXYeyvsYTW/s3kLJZcmVMPZirA3K0j4y0g77 12dKnZ6ro2T9zmWFZzpAKbUzihWoiXIzBcu1DbvheJZZoCBYG7cRTrlbkQB0 26WcdarrsCnGsrlhYy/8bPUkON5FH3VThmeejH2E7PyLAQa1Bjgs7RW+M++D ZqfVZzwXGeGDocpGteR+CP5D3PEyzBjV6HnjIpEI+t0iciK7TfDGybITXIMv 8JzYd3irm+EUFogCIwfg0zTnDN/GHC9Y1Jdq1g1CSFR36y6PLdhbVH+9VW8I +IyKcHaiBc4Ftd81/nUYymnGh3jlW9Fkt9LCicoRkDBd70heWyIzRy/gqdYY CNZZhzbNWWEY3Vv/k+c46GZvUnm5cjtuGjmo0rFvAq7UVnCjjKxxxbIJ5frZ CQg5/CyvzmUHKtTc5f2UOQldNOaKCH8bPGVZ2bXY+RuY5me8f5ZiiwWUD/fP qW+gE+f26u8yO5QMr1n+Jf1fWDvISL7VsBPL3JjyaQ5iGMoUrO4Z3YWRrNj7 pV/EEKb80OCKDKJej1NnbqwEbCpVvXXiEW22x6TRLKZgz8FKxtTq3eip82ZG tm0KzLwVm99yd6OkMakvJFoKdDWPur6t9pihcOwC22Aalr84eFm+2h5XCMty 5OqnIY9+6DGTwUDF36Ldd5ybgVLzgJnKdgbKPDnG69OYhbPrWT1sTwcMvcNL 0qidhSZjyldz3AGrTRKU1c/OQcL7VD/5yD2o7hS66aradzjOS0J9RUcUmLa0 Xar6DoV3GjqD0h2x+B4YiI7Ng0WrRDBCZ6IXb5s6fWEeMjmJqXk5TIyKzY4W 5C9AZnrI4WsWLCwcpN9V20vA0EPuM6+ChQlZsRzhfgKjXxsLFlWy0I89aljk SkBclBLiVc3CtVVVxfs8CLQErxIvqWVh4s2jDTd8CAQZLev3/4eFgdtuTy65 RKB7lH5cW8hC/ZiVLKVHBCAm7GOMPIUL1hFLOx4TeDFbGPBBkcKu0f63jwoI JIaOjWxRpjDFo8TL8SmBjTPJk0JVCslG9vnYKgJ2vkf6rTUpFLTevCffRuCz 16mTIxsorIiT+ra9I6AvDmm1N6EwzdbbOLeTwExT3PbbphQ6PzQrtRcS8GkT ze+xoPB5+OtX0V8JqCr/cv6+LYXpplY3XUcI1CYoNUl2UniuL9Ndb5wAx7dQ fy9SuGHv6V6+mIB5sWXjtAOFCrLtD1KkBFQGNLUPMCn8WGYbxJn98SurFvSQ orAqKHez+TyBR5w1v885U3hLV0VCCIHwADs59n4K/wO13lbs "]], LineBox[CompressedData[" 1:eJwVzWs01HkYwPHBkLaaiS7OJER00cWUW249j0HkX1nSyu6EhG1VorVJ2x5N GYnEFiWXSaGbIoxOMTJpshVyGQ5ZYcesXItiNMJv2xff83n5NQw86hWsSqPR dn7rf92D+5vEA8FbZ6K6jAlhiulOy8K7Wc7gk2UZUF3PFJtfT88qZXmDO+fp 48RMppiqbyvJZgWB9fPpKrY1U+wTNFl5iRUJ8rnLdSVhDPE7s3NOSaxYiNWe PcPsni/OWeIRl8BKBU/TUCtzyVwxT7N09XlWHhhURTJDctTEe31vFI2OCUHG CPQQRA9WzSM8rqt+FXBfKqV9IjmYeH7of54oAecaJ4fEaBpGvbGB9PFXkHKa 7SU4Nh91hFpdKioNcD2SZ9dUsggfyZzqGuybgePfMt8ljoXVodm6vsMtELS8 5r7OKgOcWOXAfHCkDTLpnOmuNUaoqixYqGvSATVjwWbqI8ZoRQIe7S7sBMYz RT/t5Gqsi7V4U2PaDepJuXqmn9eiQcqQ8u6HHuAMONzvz1iPQ5PdXa1sGUTU /tjayDDDvMGK14yLvdCTVlp0vJ2NDL3bH+VyOcRwRwS2KzbjhV/KQnKM+6CO vUvs4GGOCiyQH4x5Dxk1de2sNAuM3CwRLn3eD4c0aiPKqy2xu1CS2GQ4CC+9 4isGNKzxa2hL5tqTQyDFy/szOVtwneOc2ZCKYTDIlof3htig603Dn4t1PoDb k3sQfsMWo/T8jf7hfoQdR99aqLyww/XDe+a17RyFZIbpw9Eee1zEHNWUTI2C 2ni5/4j2VqRXZRatzBqDjE0WP+RvBDxkUfF2LvUJnl3b+NsKNmLB9sCcp4pP oB8xybd/gTgxtGxh35XP4JvbE5Xk4Yhlu13VUp3H4c8a/0GJ3BFj3PjXhX3j oOEWdcr/KAcN37m35/InwDbOqSlPwUFb69hU1mYFdOw/kVYb74Rc/QalilQB Yb1nGzMWOuPE6yRZOG8SlDnNwS65zphO94v0Mv4CrETpbdE6F1zUVXZTVfIF ROLG/GXFLqj+B8/bJkIJZQmVyt2O25B2169Ipj0Fza+emCb9tQ2PZRQlaVdP Ae+sQ4dgrytWrovX1Ar7ClvYHX8X9bmilvux9WcY06BqoTg+GOqGnRsapdGi aUgo3pUxq3TDhwIwlvvNAL2QHvV9zHbcV2SlpTc7A0L1kE2vVdzxNP8Gr/Pe LBgKThjqJ7vjg369TMYOAtZsI/dabQrjs/kBXbsIyDj5rUuXUBjkNWJS6EmA u+DavkAdCpeLRA93+hA4X9gWqNSlMCH5p5oLgQTuUFLOahMKD1pdG/sumkB4 u9T3jDWFRrGL3ebcImBpd2DYkkvh7JZTC9ruEGhc4q3J86Pw7Uhv860CAixa 54q6AApTfEr3bSsmcLOkzDUwmEJi6vUrX0Qg1bH48MUwCjubkgVqUgLOUL+4 7zSFj+MmD0hbCfhUlk+xz1KYaue/NredwIM2z3e/8ymk8jcKOV0E1I/z0rUS KCw/Uf+KN0AgcY/Ge/vLFF7ZYJnsOUwgVhhQci6NwghZlrfhRwI2DUdONl+l cM2Ow93icQLNVXm0g1kU0lVa8lImCUjbG5+WCCjsKbMLDZj69jMXRs/kUCgK zTVjzxAYGfXY5JZL4VWDeROEEChj5/97KZ/C/wDKSFZq "]], LineBox[CompressedData[" 1:eJwVj3k41HkcgNH0JNqRSWkShYhIikji83GU2/wcpcvxODqk0I6kZ/eRkKRB ZUu5azok14aU0VBqV8JiLHmmUbIod2swZL7b/vE+7/P++WoGhnuGyMnIyLj9 4H87hwy11X0JsS53F+lJCeHT7NZE9DLtIdXX5+bsdcI3ycvMfsL0huy9075z Gwnfpbnr9xxmMJimNWmqUFK+T/BM7TUmG8x999UX5H/nf9iSZMdhJkDmeJjE yE7Cz1/JuniZmQGGRuPT+1O/8ePkn2xMZnKBm/mw0H9ewN9/oKB0YrICkhnW TSOrZ0CRxB120ODDqKNLyNZIedTxGBt6ldIAsUodhbsDGRjdYgGZU43AFupE agyuRtUKZZGsbCs8Cz7qLOzSwKo+u3etu9pBy3rQvuuqFr4MzVE7MCKA5jXi 3NuZOijWtVIqPtkFqlxOkoWfHspJipar6fSA0w7bEm0vAzQjAVVeJULgPuiB cEUjfJdg2vJmUy+ctVCqbt9njOvShyWFYx9B9EehIaduKw7P9Io6jftAZfQx 6aabIPdrzVt66mfQ1k+dhDOmSFd/MN7f3w82L1Kyrgq245XjlUfyNwyAf64L 8zjTHKexqP9Y7CB0qgRVKpzdgextDRWrXg3B2o5nnQu1Fthb0pDSpvkVBLRP ekTdEudDBVn654ahOqWqJuvMLjSwWSI9UjMCfLnq3oCnVuhwR/NoueoY1BNT 40QGYLS6v9anw+Owzv0fDsMA0XBkr2KX2wSU9qsmJTYirlCakG+Ym4CeA+FX IMoGafysUu3sSag801gZsNIWT5jWvF/q8g3+vJ0R1v7SFoucAvNfTH8Drny+ P+2kHYqH1ywfuPEvfAl/IKxQtMdKL4dFGfZTILhYp1z/1B5jHRPzKgam4NAd k2ve+3ej5gfn7ruJYlB6xPF/Lt6NO80TMpjbpsEitmb6Qv4ePKzRKpHtmIYZ dnNFDzig+C2nLyJuBjD81bPMEQfMpPmxPTfMwtOqVc+HOI64QlR5R65hFlga 58sZhk64+Nc4b4tICZSJcobvdzmhTKFfaR9jDpKy8gZaop3x9O1SDuPlHNxU WH48SMcFaw0uySufmgcZccTfglYXVHY+bXiB/h3kHq+Q6TnlisLNf3XE8L7D emWelbuaG5blwoZ+vwVYZu7avZfnhr6lZsrq0gXgWp8vtjjojucTC+KEj6TQ ZK2YmrqYhcVD6ll0VwKz77OORt1j4aWcxACRO4Gr149FwUMWBnuO6pR4/Gjt 2vilRSxcy+OVufkQiKpdKMgpY+HltENvrgQSEP0m7H9dw8JjZrcmFWIIKBfQ E1a1s1ArQcVxyX0CbUHGetVSFkp3/PJT10MCbw7GaNfLUPh+9HP7/SIC6ahh oitHYbrPE9895QQkliZeEzQKySbPnxN5BJbVJd9IUKBQ2JaWu6iDANtvUL94 JYXVF2eCOjoJzJ+Lt2KoUphh6a9/t5tAuFmQR/RqCl3uGVXYigiMxY3G2KhR +Pxsc2PcFwJNWze3dK6n8Mbm7WkeIwToywY+79SiMLIv21tznMAtdp8kT5tC Pdew3ropAh8G7+mG6lJIkxVw02cI7BoLs2rdSOHHSsvQgDkCBueivU31KeSF 3t1ivEAgIvn1iVubKLy5TlFMyI9/pk+81IDC/wDyalnE "]], LineBox[CompressedData[" 1:eJwVz3k41AkYwHFKi9XKkXomUXLlKg0RyvuWGsyM5meIehbNY5WjUsmzpUeP pnVUiJUt9zU22VlXjt1lHMVWRGRYZlfDMo+jcRYzUfy2/eP7fP7+GgReZJ9Z p6Cg4PGl/6WfmXzTMnXGOUT3+s5QgyZnJZdtl4YpR4HzU3lCGi8bbPIzcqop 3kD3T7Hy5vGB0TXwJJcSBC9+oFRY8RrAN0jemEaJhNiUYovVolfwdm+CSzIl FhLSw2cuFv0DBTqs+LuUdOi8xM73KZACV6Xa9A6lGJ48yLHSzvgEJ08VVswv 1EDpnzovA3I2ohrJ9XPVbwbVKDfDGIoOGnvOTrYmtkHSDqo5M1cXr752gIzF djhZ1dB7GA1wa42mWFGxG1YrzgULOUZYN+rS2X2wF+iNnZt/45vis7Bc3VPT fXBT0OpxvMscl0wObSq7MAAcuaWJsMAK1y3zNXSN/waLA41SG4Y12pGcOq/y IZC2+tDuFOzDzljb18/Nh0Ewn3m7VkLFHanS5dLZEdiQW7sv2dEWpfJhcb/1 KMzQpl4bRezH4ncNHer3xuCK3S32WKMdquuVzEkkErD24oocSXtMCq09W2A0 DvK4V/qM3Q4oQ74kJGYCbL73FZSFOGIkta1mS+skxImzYp+mOeFweVviG4N3 0OhzM4/dfxA/hfVlm12Xgud4oaWGljNaHFZeO9swDYqhvfGTDoCuRQbBVVtn 4YLqUyg5hHhV7/Suf/3mYLv2fJN2H6Ll9Am1AY95iPp1IUkWfBi1N82rtK3M g+biYOyEyhFUas6uMMxZAH7PY/HD/CN4zrZBpMp4DzrP5+auurgg3z2woEn2 HgS0v0reSVxwSbpNY/zBBxhLitijEH0Ua71c16cfXYS6JUfR6Z3HMMYtLr9m fBEys1pmGfXH0OAtfZAXtwRK7cYK+Z40dLSPTadQZeA2u4HrLqOhn373sqJQ BpyPdlSfVFdc6kgevcSVgzmzfuKZvRtmKAVEso0+gquaallUnxtqi2uL1rV9 hIXycMMr4e644QbX2+HyMiz0XH7Uo0NHhdKAilGtFVi5l+fj9YSOEVkVyVrP VuCFRZq7sx8DGy1uq2iGf4I/cn5U9VvPRE16hOUt9c8gLPFnxuQzcciqRxgl +Ax9VUNOG909sDIPjCQBq2C6nKmRMuGB/hV2mnprq8BbOME0/uE43owr5A79 sgYJkdGBJpYsLJvUy1ZnkiAKavdQ7mDh7dw4jvg4CcGGvYUvO1kYxJ4xLvck QVyotHynm4XbBYJKD18STEzHKjf2s/BuyrfPkwJJaOacp2mNsDDELnPh6ygS eldGlPVlLNwVu9lN+REJZ+dls7qaBK4diP5m4DEJKs3VHdFaBIpmxnof8Um4 IZKVvNUmMNW32p9WRQJhph6cv4VA0px9JU5AQk1LpHzXdgKH3qTkrReS0Fna xDE3JfD3ePl3wn4SEhX53om7CUx3Om3GGySh8v4W+rQZgYyf99QcEZMwUBLq UG5JYP21rnbuFAllfh/MqFQCH1jtT/GcJiHeq8vsvg2Bl0dzvA3mSJhSNbRY tCVwN/P8cMsiCfdWgFpnT6CSYl9xqvzLn+9XB7Y6EDhS6xTGWSEhq54G1xwJ FITx9lqvktBWo+AmciLw4Q61JZIkwXPQhu14iMD/AD6nUsY= "]], LineBox[CompressedData[" 1:eJwVjnk41Hkcx0dJJFeXHSUNodIhacoxPh9HKUeZ8Zu1RYiolKOyj1SyWtQW sj3WkiO5SpZRM+RhLMnToZKiHM9EDY9GjsSMaYjv2j/ez+t5/fV6MwLCOUHz aDSa+9z+p0uQ5E3DYJCdrDN1aE5R2VEvopfuBEZJDw4uZNJw262MbD6dAtPz W0N0TtLQ9VXHgxz6ETCp+51j3klDryPyuhv0SOhu8b+VUaGEH7Zcdkymx0Os QvJQI2A+5i3fn3iVngZVNfcbvZ+qYJwq3/QPeiGk105tGM3UwF8O3OaNfRPA QJjOgds2K1CdxPk4r64H6afttcnG+mjMHpU8vtYEn/kTwfmDDIxqsYIM6XO4 YM0IVok0Rl2BTo+S0mvgm4W9F5Wtwyqx48vXtm8hdHJmunzlRmwMyVl5YLgd Hq1Ry64I24IyE5ZWWWgHeLPkTjSHrThPUaq90rgbNNxzay+OWCCT+Fd5louA RZs2Z8dY4st4y5YnG3qhP8oA01SYaJA6pCgZ/Qj06PBMbf4OHJL39rwzF8M9 +8Pd95yssPBLbbNmSh8EHtQ1GFJYo6b+na/9/f0QeoOlWFBii0nHK4Pz1g7A Loam401bO5zE0v5jsZ8hv2/Rus4JwEiLJsGKxxJ4dP4vs5SniL3lTdfeML5A wgu/cdode5wOac9af24Iwg7t1JNeckAz+4WzwbXD0PajtSLTwxGd8xlH7+uO gmibqUzJ3Amj9P0MP/l8hXE/9oCctgs3DnPVO9zH4GKVxVujll24VGtMtWlq DGimWRlqZbtRuT6LZ5T9DTws63U9YpzxhGVtl5rrOOzMHfyyz28Plu4NyPt3 chzcujPhBGsvyob0tAfSJ0AvdtWCZ4tdsNLTeX6akxSWJQce7Rpxwdg9CbcE A1IQJec0r2pwRcYHl86CBBk0Rqsc909xQ+sd8Wl0i0lQ880a+TnMHX1Wv1Yo tU2CaoPtklDYh7LmZHFEnBxCncuKmIb7MUPZN5Kz9juIJUlrdCf349Keyvx5 Td8hd2LEWhrggQti4iirUwowYZmdqmrzQFqJL0+8ZAqMvX71mbVl4+mbvOQl jVOAzYmWa3hsrDO7oqoTNg3lRo+7dxhwUMfl9MZLmj/A6GT1w9bLHBRtam2L Fv6AiG0zuY4KDlbkwtp+3xlwe1KXsz3QEw/xmDr6szNQX0UZ0l944m8Jt+NE 92bhRT5L8t6GwjKJfpamGwGBXLNdu4jCKzkJ/j37CEjtKOFAMYVHOCPG5WwC fTVqRcK7FK4SCivcvQgUdzZFHfuHwqvXvZ8kBRAwDTpr2MCn8Bgz89uiaAJC Xk1SeCOFhvHL9iwsJlCf/YHf0kvh7M4LGh13CbhrjZUUfqKwa6TvbXEpAT+1 8LxzfRSmevEP7b5PgMF4kGLymUKygXMmQUggWbg34uIohaI313PntxFo5RU5 b56hsDpRHtj2jkAF84yTMqEwzcZvfUEngecxpfbdNC66Fm0WOPTM/RN5sxKV uVhz9tXzuEECwc+qrXrUuZi+aft19jCBP6HLSqDBxVPibIrxlQBJD7S+qsXF dW4nexukBA5HVdoyl3JRWam9MFU+1392wW7xci5+rLQJ8Z8iEH6tDMUruCgM KdhiPkMgrcDZsfonLv5toC4jhEC2zGV3ih4X/wNBUk6x "]], LineBox[CompressedData[" 1:eJwVjnk41HkcgGcY63owQnacO2LXVWYpVsrnI2fjCr/JerZEUVGS1j5p1Vot KkdNLa2zaLC11pVje0pY5CnrSPQozzQKyd2MxTDFd9s/3uf9833ZB2MDI+Vo NJrvJ/43N3Kyv3Uq0tmxgx9DozGR4ap3coTlBk5LzSI2i4l2N3ML61gUyDn3 hHrYMtG7Z+huESsCPMQLGbkRTAyOkD68xoqHH1qVC8OfMPGVzQXXLFYKrLbd zEr7VROLdfzT0lnZEFzbBXqWWpisVPfVJVYpWFi6eLqHbcRvQ0qqxZJ6UOKY xwafNURVkrzP06gF9HOdS98ZmaBZwPxke0YH5Pwikw1GmeHpXkfIXXwCg6pz ermD5qhbrymi0/vg9Rwj2+6xFTaOunb37XgGkijLPLdHW7Atukg/ZHYQzqmV aA73cnDpy50alTFDMDYh8tHdZItyqxVMfbNhIKvGvZJ8O7QnYY1BVUKwZTje o8lvw+6Urb2dliOgMr5w1jrGHo35M6t35l9DFpR0thAHnJGOiJ5zRsFSQbuL k+SIpdMPutQvj8FwuEbiUzMnVDf8/f34+DhUToiF4V07MDOq4XCx6QR0+xrl CPY64zJWjB9NegeaE4nhUnnEeNuO+o3tkxDSG9Z8vg9xpKojo589DXfO2yg7 V7rgh+jBAosfZ+BUvnB46sIutHJRXD/8YBZOFDPoAsoVPW+xj9TqzoPZ/RQb Vzs3PG14wOTNvvdwt/NqdLm8O1rP8lSHfMVg0WXsceCpO2ppiJU6ZGJoSfEx eFPlgYyWgupNhRKI266dKfzJE49tffBS2XsB+PnsxLwwL6zYfbC4eXkBQtdP Ryc778alGT3mxPV/QV65n9aoxsWGIE/5bLdFoBfohgrmuZjklXqzfmIR+LLw 4a5Wb2S/4r4QpC6BRqxCgvSyD253SMlm2S7D32pG9JcnfHGfUd8qfWAZuFo6 AhH44VJX1ujJZClw09fV80z8MZcRGh9ougJRsUdSY5b9UUvUcEuuYwWUJE6h eof2oMK5ZMoxbhUeJSqNDA3sQdqd0OrRDTLglqXLGewMwFP51Vkb2mSQzW8M 2F4dgA+tLippnvgA0wbuMj/jQNTknrI+r/4R7hu2R729EIjCzU8HzjR9BM6i vcLe1UCsuQGm46Fr0OxFmXocCsL91faahutrEL+yX8X8nyD8ObUkWfjHOnR+ scNt3InCyknDAnUfAtCtP21QRuHFotQwkR+Bv/yVehbKKYwInDOrCiAQKTxS 8/g2hQZNTTW+wQRcriUlxP9JYfqV7zozDxKQrKipd9dReNQ+T6JyhkCLcYZf YhuFJinaXorlBEwE1qbDIxSuf3NWbeg2gaK8nTo1byh8OTf2rLyCQEXjw8/S xijkB9ft96glYDujMvP1OwqJZeD3qU0ExPPP712ap1DYf+WG/AABurp2lOMa hffSpIcGnhPI8VEO1yAUZjsdsBC8IHC4/1jIWxoPvcu21O8SEbB2SPC+yuDh /YSeJ8lTBDIdKrZOqfLw+uZtVwJmCSgeV+S0qPEwbrSQYr8nUCnrs8rR4KG5 z/GR1kUCWFtm6qLFQwZ9sJQv/fR74y5bV4eHrxucosNkBBzirIznNvKwKVpg w1kj0KrKNGz/nIe/GasuEfKpHxCmn6fHw/8AuW5Bfw== "]], LineBox[CompressedData[" 1:eJwVxXk41HkcAGCiTLlZMoQdpZRBtVaK9fkIkaOcOX5TjtK2attIT7G1cttS bDuJZiqk1pGjHOtB8TDZtBU5cqSh4bGjcZZxjOO7u3+8z8sI+ckzdJWUlJTb f/7fOVT4tmE01KaqiB8oJaWFsnbaZwbo9vBsntu3rKGF39zL5JbTvUEyXXB2 xVgLXV53P7lDPwYF01EKa/200PfY3NMb9EhoObGBaV+mhR/Mku2u0RNgR41P s3cwHbM1DiZdobNhUSZcU/xcG2Np5Vt+pefBfEj/kDBLF/38c0qnpitggPY7 lyZhoDyJZTnq1cNy5ETttLYhGnpMCJuu8uC2weeGv/yN8Pyb3ZA50wKmAhpT SYOJ6ytU+dLSrWBSJ2ca1GCGVQK7V63W7cA3ZYcbfdmBjWF3dPzHOmEwdbR7 UNEcxZu/Uy7+sRsU3m9/tFnFAlctFKnoGPZBmF6PS5ijJVqQoCqvkn6YMTOS 7wjcg68SzN80bxuAgj+5I1kR1qifLloomBgE9xfJ+a+qbFA0N8Dv2i4Aq8aZ fWUnEfM+1b5Uuj4E7Tp9adZsW1TS/WNyeHgYYrM2+sRV78XUHyqPZ28agfjf WIfGW+xwFouGT8T8A0XiBTmbL/YYuZNXodkkhMibNr0Ba/fhQAnv6lvGJzgt iZN22OWIi2GdnK3RIshhF78wDnJCY1u5leO1Y/BIgaWbdG4/OuYyvn+8fgKC d8k+uJnrjOd1Aw0+siZhZ6+kZbbWBZljPvLdblMgEnCKldpcUV15isaTTEEY t+RJ26IbytZzSjdyp8FWXvR1vfpBPGle27vW5TPU0LxyChnuWLQ/JPvZ7Ge4 0bCc11zljmKRtspIxhfgFL+JGLP1wEovRxm2/Qz0FZo7DPd4YIxT4r2KkRkI 5NETBkM9kfHBued+ohguyh//22DKE/fsSmDTd85CgMmCg0WSF7L0WhekO2ZB pByc5KjmjeKX1wRnYufAva5Lc1uhN2bKHon03DQPg9H57nKWPqjOr8xdxZuH SqtGWcMmH1x9KdZ7d/gCCN679akHHEKpgiOlAjUJtMYrui2MHMKI26XX1Bol sDovX68sxhefGqfQVE8vgvHHpNQHGn6o6hzBjFNagvJot8jrOX7Yb9LWEVW3 BGdHFF467fbHsruwafjIMoQ4LemLm/3xcKmFqu7KMqg5cNZ/8AjAy4k5sf2F KyDc8kt2hjAAi4W6HCVXAkPvavTxHIUpdxKD+AcIOD3xtak4T+Exz3HDEg8C jzttDxtFU7ihrq7MzZeANWeZoxJD4ZU0qjk1hIDmJxXdjykUnrDIml4XReDU JbZJHJdCg4SvnOQeEnANv5zMa6JwxfKiYnc+gQtH75ZaNlPYOz7U/rCIwFUV uZ5HLyhM9y0/vO8xgXqX6q03X1NItnmeTawjkKGd2RbaTWH/27S7Mh0EPNqt mHIiCquT5o52dBHIZS75/TxOIdsqcOv9HgLJa9YkTU5S6PLAtGIvn4CBSDzY PUNhzYXXLbGjBFT87G/nr1CYYfJtmscYAZ20Ay0bpFkYLuB6MyYJFBXmzKfL sNDI9dRAwwwB570GflE0FspKd+alzxEQ3jqYMr6OhYOVVmFBEgIbE59XByuy sC7svtn2ZQLts/GjXcosvKUvLyaEwLveK9rOaiz8F2HWWLA= "]], LineBox[CompressedData[" 1:eJwVznk41AkYwPEx7FKtO8vE1IyjQ8TacnS9b5HbxriG3+SKDrUrR6uyHssi EXlkVUuHo2tUVDMqpmVjFSWN4xmKIclODEYxcv62/vg+n3+/zLAoVgSVQqF4 fOmrrhESYd2HiO3HNANWUygMVLJfcaSP5gDyag/ucxUG/nj5fNF9mg9c91jo O6fJQLcW0b2LtHDY8z4l3MqIgf7h04/zaHFQU+Q3FuXIwF6Lk/bZtFTw5j0d Vc1m4BWd3emZtHxIS5QRvSuYmKxyf80pWhl8qx1dq2FniOyA4grZBA8s7lrH U/nGuIxM5jitrIW5tUmDVUZr0MRrTFKf1QCu1XR+FG8dxr+0g/OTTRCSqhX+ g9AMdXmaYgWFVtAQbCp5oGaJVQP2L1q3tkHg4VB+s7IVPom8qB8g7YDiBUlL sO5GnFq9Tf32zyLYH8pqlC+3RupMuYa+yWt4ZFb2UeRii9ZkSJX3nR7gOpWq rw/djC9SN75sNO0DhvQGOyx2K67KHZm5OdYPNiM6dfhgO45M94k7LQfgFtXG p+MQYtlwTbNazjt4mffmKSt/B6rRr48PDg7CsFgvJ/fhTjx9kL/vivEQsPKP yuRN9ijH8sEDSf9BtalRjMMnB4yzauB9Xy+BA6pMv+Aljth3pyFLyBwGFvWy gbONE85FdhSuOzECWcWR8+Yhzrh+h/LivhopyPRRcPKoCzqVMPff1R0D9RhR W0GJK8bTgw3fcsahOJR6e7rGDc2kvstEHjLQMjEj1F+5o7a6TKVhVgZ5+m2b hHMeqFRbWGFUNAFa/3an12rvxkMba7qXuH0EFUniMy7TE8tdwq78Lf8IIZN/ 1DdWeeLUyAqNoYJPEEm3yJLu8EK+t5NivsMkbJPGsQe7vDDJOe0yb2gS/HjX zvZHsJDZ69pVmjYFExTdLkMZCzfbpObTrOQQtdzW0zrdGzkrW2cU2uXACxPm OGn54FRz9sCR5Gng5lbRTbk+eF4pKI5l/BnuvQnyU7b1RW0xv4Ta8BkudGYu Man3xW8Sk33someAUNkl1g70Q8rNoIoBrVnwPRzhOTPkhzF/VWRrPZmFFJdY ZmWSPz5en6Gi+csctJn151zVYaOma4xZito8BNru/jWnmI095q/ajwvm4R9B 7XNnuwCsvATGg0ELIKyJZk41BuCeCmtN+uICBHzu1ev1CsTf04qTe7iLUJCY V1wgCcTbEnqhmjsJoTe5DDxKYMbFtBDxTyTUjTkCL57AcNaoyR0vEk4nWAat PUGggUBQ6eFPAlNvpEgjicDMM0Tj6TASFPXm6W8zCDxgfWFi6XESKMyEDSlF BBqmLndWvkbCNvegjIZ6Ahdtf1MV3SBhDT+h0raRwO7Rd23Xyklgd7/ruvWM wFz/+3sc75IgVcw3/bOFQNKUFZsmIIHkRwsjRAT2CM9cUmwn4cMuTXPlEQIf pk/vbe8k4b2BMCBhlMD8LcHrSrtIaI19nT4+TqDb1Q28nWISMr2b3oomCaw+ 1tKU/IGExWqdwhuLBBaYbzrjJSUhJ3pVs4ECB6MHinyY4yTMfRczk6vIwbXu h/vqJknYe3WCfVyFg0oKHWW501/+ElaeGl3KwX7+lsiQWRIODp99FKrKQUFk qYXlAglVvV7DneocPLdq2RRJklCxk63vqsXB/wE+T1DH "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->{391., Automatic}, PlotRange->{{0, 2}, {-7.999998857142868, 112.28577312106312`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{{3.470311827731405*^9, 3.470311899247405*^9}, 3.470315064742637*^9, 3.4703724008850527`*^9, 3.472291944523514*^9, 3.472291984557514*^9, 3.4722941707070656`*^9, 3.4722942082963066`*^9, 3.4722951757335677`*^9, 3.472295406348627*^9, 3.4722954790628977`*^9, 3.4722975818764*^9, 3.4723008994348*^9, 3.472301348668*^9, 3.4723141667410927`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "0.01"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ SuperscriptBox[ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], "2"], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.470314887325637*^9, 3.470314898389637*^9}, 3.4703149400346375`*^9, {3.472295253647358*^9, 3.4722952552145147`*^9}, { 3.472300922008*^9, 3.4723010013964*^9}, {3.4723011265864*^9, 3.4723011439491997`*^9}, 3.4723012799344*^9, 3.4723013158456*^9, { 3.4723013799772*^9, 3.4723014335632*^9}, {3.4723122574876547`*^9, 3.472312275438655*^9}, {3.4723124656116548`*^9, 3.472312465617655*^9}, { 3.4723140885346375`*^9, 3.4723140936391687`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7H+kXxcUvpdtDxVwCOArVCq5PRfK53Dg2Hm4 7mjhbihfwMHvYEn0RJczUL6Iw7JHk0WWXr8I5Us4xKLIyzi4oOhXcGhBMV/J ITQD2f4PMHfAgAMqlwONL4DGF0HjS6DxZdD4Cmh8JTT+4AkfALoZUiQ= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "7.720679681477542`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7MOnZhT2XpxjDxVwECtmX7Ui/iCUz+Fw6Cw3 85bUM1C+gANfZL3nY4e9UL6IQ6D7GSuZdHNLCF8CTV7GYTeKfgUHQRTzlRxa UOz/AHMHDDigcjnQ+AJofBE0vgQaXwaNr4DGV0LjD57wAQA1nkvY "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "5.651544001644865`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7G25Jpt7iO2yhwo4SPxf+GOWzRkon8PBQvj8 5tpjG6F8AQdfafau6ZfmQvkiDktkbzjEmR6B8iUcFqLIyzh8EULWr+DAgmK+ kkMuiv0f7GfNBIGVcPeg8jnQ+AJofBE0vgQaXwaNr4DGV0LjD57wAQCAxnfD "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 4}], LineBox[{15, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{14, 5}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.05}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "3.6015476226204512`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7Ccm7zi79v8pe6iAg5Lf1U95y/ZB+RwOqfIu xy9ZzobyBRzsCr/EP3A9BOWLOBznUuVPS5pmCeFLOFijyMs4PELRr+Dgj2K+ ksMNFPs/wNwBAw6oXA40vgAaXwSNL4HGl0HjK6DxldD4gyd8AJK2WJg= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "1.5709554206447685`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7C1fL98+t+KiPVTAIf8Bex+vrAOUz+FQ8jK8 dP6vw1C+gMPuyjsBjAVCUL6Iw3FLB+kS5kNQvoTDkixkeRmHOBT9Cg6Gd5DN V3IQRbH/A8wdMOCAyuVA4wug8UXQ+BJofBk0vgIaXwmNP3jCBwBr4E4G "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.43995503035399164`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7FOKhffUfDljDxVweDgl0TkubCeUz+Eg2Hu2 N2nSIihfwOFH3Im63bsPQvkiDlani1MmxcdYQvgSDn9R5GUcTvYg61dw0J+K bL6SgzaK/R9g7oABB1QuBxpfAI0vgsaXQOPLoPEV0PhKaPzBEz4Aj41WuA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["2.4308924206796787`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7Nftn/o3kHGfPVTA4QCXzNJLa05D+RwOM3/P PWXXsgbKF3D431SzIkh9IZQv4hD2esk/+/OHoXwJh70o8jIOz1H0Kzi8QDFf yWExiv0f7GfNBIGVcPeg8jnQ+AJofBE0vgQaXwaNr4DGV0LjD57wAQAK1YQH "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 4}], LineBox[{15, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{14, 5}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.05}, Frame->True, PlotLabel->FormBox["4.401550544974307`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7M0jZRT6jy20hwo4JEnf3fVh4SEon8PB2HsG Q2XfaShfwGEeG/vPJ7t3QfkiDsopS6TztzZYQvgSDj0o8jIOjCj6FRycUMxX cmBBsf8DzB0w4IDK5UDjC6DxRdD4Emh8GTS+AhpfCY0/eMIHAJicTnw= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["6.351607001609971`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7Bkf91g9zS+yhwo47DSc7iitsxDK53BgSc6r jZuwB8oXcLgtx8j5c8tpKF/E4WM1775AlYtQvoQDtzyyvIyDJYp+BYcbKOYr OUig2P8B5g4YcEDlcqDxBdD4Imh8CTS+DBpfAY2vhMYfPOEDANOQSiA= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["8.280721728769727`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{{3.4703148898906374`*^9, 3.4703148993466372`*^9}, 3.470314940657637*^9, 3.4703150651786375`*^9, 3.4703724026321516`*^9, 3.472291945395514*^9, 3.472294171068102*^9, 3.472294227658306*^9, 3.4722952627082644`*^9, 3.472295406548647*^9, 3.472295479161907*^9, 3.4722975821572*^9, {3.4723009234432*^9, 3.4723010027223997`*^9}, { 3.4723011279904003`*^9, 3.4723011464608*^9}, 3.4723012844896*^9, 3.4723013170936003`*^9, 3.4723013495884*^9, {3.4723013812096*^9, 3.4723014356224003`*^9}, 3.472312313924655*^9, 3.472314166847124*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "1"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], "^", "2"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4703149605826373`*^9, 3.470314984936637*^9}, { 3.4722952583588295`*^9, 3.4722952591509085`*^9}, 3.472312322012655*^9, { 3.472312465620655*^9, 3.4723124656256547`*^9}, {3.4723141004652157`*^9, 3.4723141027779093`*^9}, {3.472314208595645*^9, 3.472314209291854*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7IMNz98u/HnSDirgsGZ1z4foQCd7CJfDge1p leZt1elQvoDDRbH0NenvzkD5Ig4Bk5rPWPA+gPIlHFRQ5GUcRB4j61dwUJ2A bL6SQ9P9fUj2f7BnQAUOqFwONL4AGl8EjS+BxpdB4yug8ZXQ+IMnfADHA1Ts "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["17.996024243388117`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7OV+7P+QLsJiDxVwWPpT4teR7hIon8Nhh9C7 xZPk90H5Ag5lk+7M91a9AeWLOFS6bVfjuu5rBeFLOCxHkZdx6OJF1q/g8O8C svlKDmw5W5Hs/wBzBww4oHI50PgCaHwRNL4EGl8Gja+AxldC4w+e8AEA/2xT ZA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["23.63060215541256`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7IMnC1XzrVK3hwo4TN9Wrvxy3UQon8PBvy53 mrnNGShfwEG8+uH+RSVboXwRhy+cUxLXn70G5Us4OJYiy8s4uNUi61dw4NmH bL6Sw/SJIkj2f4C5AwYcULkcaHwBNL4IGl8CjS+DxldA4yuh8QdP+AAAgWdP nA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["28.337955230290568`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7CtNpspwF/jaQwUcxCOMtvTWrYPyORyOPNlS NLXtCpQv4OAldsulOXsflC/iwIACJNDkZRzuo+hXcJBHMV/JwcEQ2f4P9qjm MaCZz4HGF8CwH5Uvg8ZXQOMrofEHT3gAAIcaRRE= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["32.97005207498968`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7DVi2eZ2TvW2hwo4TMx7rfyldiWUz+EQqSWp +fPSCShfwKHCZO5L07XHoXwRh9+bkrfWcB6C8iUcHsojy8s4yHMj61dwUE1B Nl/JIVmDA8n+DzB3wIADKpcDjS+AxhdB40ug8WXQ+ApofCU0/uAJHwBgIFCI "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["34.24759216479473`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7NPVDy6rXjjZHirgkLqwJa9jzi0on8MhX6jw zjTf9VC+gEOibPOB2mv5UL6IAwMKkECTl3HoikDWr+AgdRfZfCUH12Bk+z/Y o5rHgGY+BxpfAMN+VL4MGl8Bja+Exh884QEAe6NLgw== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["42.82743386708951`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7A90RurrdE+2hwo4SCU0+67NugXlczi837+H cerH9VC+gMP/+107F5uXQvkiDtNzjdY3yAZD+RIOC/IXIMnLOLy7fR9Jv4LD w+ULkMxXcvh+OA/J/g8wd8CAAyqXA40vgMYXQeNLoPFl0PgKaHwlNP7gCR8A UqVXWA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["42.84649289932804`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7F/pn1ndv+2ePVTAYZP93Koc8SlQPofDkX9i oso+9lC+gINzOv+vrZ6P7SB8EQf/Ka49+pfSrCF8CQfdhV+fIeRlHP4Ul3xT gutXcIjX/5qGMF/JwY7lQC/C/g8wd8CAAyqXA40vgMYXQeNLoPFl0PgKaHwl NP7gCR8AJFdRWg== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["56.57191190250825`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7Dc7t9k3bLtnDxVwUD10+/458SlQPoeDlfmX Taax9lC+gMOb5rWz+H8/sYPwRRzMVHabygWshPIlHFYv45qMkJdxOP+SfzlC v4KDVYXNDYT5Sg5lU+8bI+z/AHMHDDigcjnQ+AJofBE0vgQaXwaNr4DGV0Lj D57wAQDxmVJm "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["56.57193546219854`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{{3.4703149693056374`*^9, 3.470314985682637*^9}, 3.470315065269637*^9, 3.470372402772544*^9, 3.472291945514514*^9, 3.472294171179113*^9, 3.4722942277673063`*^9, 3.4722952648494782`*^9, 3.4722954066546574`*^9, 3.472295479269918*^9, 3.4722975824848003`*^9, 3.4723013498380003`*^9, {3.472312316642655*^9, 3.472312323130655*^9}, 3.472314166926148*^9, 3.4723142105982456`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "10"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], "^", "2"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.470315002518637*^9, 3.470315003110637*^9}, { 3.4703164478340783`*^9, 3.4703164606583605`*^9}, {3.472295277055699*^9, 3.4722953094079337`*^9}, {3.4723123323556547`*^9, 3.472312334363655*^9}, { 3.4723124656286545`*^9, 3.4723124656336546`*^9}, {3.472314108034486*^9, 3.472314109963064*^9}, {3.472314214757493*^9, 3.4723142148765287`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7BkecIUI1PbZQgUcVs/of84lmWEH4XI4yC31 dzE8KW0P4Qs4/NKz2MSsuQTKF3H4uqrwmFLlWyhfwsHDFFlexkHTLxBJv4LD 4wlZbxHmKzkI3p536zHc/g/2DKjAAZXLgcYXQOOLoPEl0PgyaHwFNL4SGn/w hA8AfIJILA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["238.15065044287752`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7PnmfrnAmvXAFirg4HUrocxv2jY7CJfD4Wx6 ybwYmxR7CF/A4XgF38LG6/ehfBGHpe813u9LWWEF4Us4TD+PLC/jUB5RiqRf wSH1Rn8Fwnwlh0fs6dzacPs/2DOgAgdULgcaXwCNL4LGl0Djy6DxFdD4Smj8 wRM+AEK3U6A= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["259.70105425414516`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7B1+FTVsWPXAFirgcM6kTGb68m12EC6HQ3JG bNPxK8n2EL6Ag2BylMrWwLtQvohDwKGLIndNtkD5Eg7qlZFI8jIOTUvjkPQr OATlfFREmK/k8MuptJ13Ncz+D/YMqMABlcuBxhdA44ug8SXQ+DJofAU0vhIa f/CEDwBvwFMe "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["261.54791710441845`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAmIQDQEf7DlCJh9RE6yygwo4nPURFPF/6GYP4XI4JEb1 LhA6cx/KF3AwXH/morpdCpQv4sCAAiTQ5GUctLT7kPQrOGx5jGy+kkMaw1wk +z/Yo5rHgGY+BxpfAMN+VL4MGl8Bja+Exh884QEARstBOQ== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 6}], LineBox[{15, 7}], LineBox[{16, 8}], LineBox[{17, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["320.1589376821098`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7LuVAjrvClTZQQUcrt9O/PjugZs9hMvhsL3Q 1UD19H0oX8Bhg0e1p9aUFChfxOFuzTbPyakMUL6Ew64MzgCEvIzDH+9CK4R+ BYf3xxb9QJiv5HCjZcXGO3D7P9gzoAIHVC4HGl8AjS+CxpdA48ug8RXQ+Epo /METPgD3YlSc "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["320.1614241704957`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7B0b+Xdp7Nayhwo4CApnh279cB/K53Doawmt 7njhBuULOBgxuNwTr1pgB+GLOFyeYuEQdtfYBsKXcLgWfW35DLi8jMPBTZuT rF/C9Cs43Bc8eXTdR5j5Sg5canI1P+H2f4C5AwYcULkcaHwBNL4IGl8CjS+D xldA4yuh8QdP+AAAFftQUA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["420.08286472060547`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7M+7b5vUvlvLHirgoC33arnax/tQPodD/lKh onsv3KB8AQf3tckXBNoW2EH4Ig6PFlYG7L8nAuVLOHxbrTNFBi4v4zAh/9uR d3D9Cg6NExKybOHmKzlULno9bxbc/g8wd8CAAyqXA40vgMYXQeNLoPFl0PgK aHwlNP7gCR8A0M1X2g== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["420.08286493906627`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7HXisvqnsr63hwo4/G5p4lj4zhLK53CQdd3L 5HGx0g7CF3CQabseKKe21RbCF3HYYTTl6+ZPz2wgfAkHjwnPd/Vxp0LlZRxM plpnv9+sCdWv4KCx64y1+sWXUL6Sw6NZMw8GPZpnD3MPAypwQOVyoPEF0Pgi aHwJNL4MGl8Bja+Exh884QMA2IxSfg== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["560.0571433431395`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBmIQDQEf7N+xrjFXrX5iDxVw6PVQanklZwjlczhM23w4 u4u70A7CF3B43bl61rb3q20hfBGHpCtXLzhKMkL5Eg5/HF7+P5s2H8qXcZhc odC6Sy0Zql/B4cqU9pp6G2Wo+UoOf9ym3WZlvm4Pcw8DKnBA5XKg8QXQ+CJo fAk0vgwaXwGNr4TGHzzhAwD9L1K2 "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 1}], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{19, 20, 21, 22, 23, 24, 25, 26, 27}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["560.057143343142`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{ 3.470315003854637*^9, 3.4703150653856373`*^9, {3.4703164486181564`*^9, 3.4703164615144463`*^9}, 3.4703724034589043`*^9, 3.4722919457875137`*^9, 3.4722941713681316`*^9, 3.4722942278963065`*^9, {3.4722952797069635`*^9, 3.472295312062199*^9}, 3.4722954068416758`*^9, 3.472295479406932*^9, 3.4722975827812*^9, 3.4723013501968*^9, 3.472312335507655*^9, 3.4723141670471845`*^9, 3.472314216539027*^9}] }, Open ]], Cell["\<\ The atom number distribution becomes more peaked for increasing interactions \ -> \"number squeezing\" In a large 3 D lattice this drives the transition from a superfluid to a Mott \ Insulator.\ \>", "Text", CellChangeTimes->{{3.472312350188655*^9, 3.4723124123956547`*^9}, { 3.472312465643655*^9, 3.472312465656655*^9}, {3.472313466090655*^9, 3.472313475221655*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Single particle - 1D lattice", "Section", CellChangeTimes->{{3.4703194710615835`*^9, 3.4703194793334107`*^9}, { 3.4723124353696547`*^9, 3.4723124370886545`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Hsp", "[", "Nl_", "]"}], ":=", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Abs", "[", RowBox[{"i", "-", "j"}], "]"}], "\[Equal]", "1"}], ",", RowBox[{"-", "1"}], ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "Nl"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "Nl"}], "}"}]}], "]"}], RowBox[{"(*", RowBox[{"Nl", ":", " ", RowBox[{"Number", " ", "of", " ", "lattice", " ", "sites"}]}], "*)"}]}]], "Input", CellChangeTimes->{{3.470319517915269*^9, 3.4703195992353997`*^9}, 3.470319732209696*^9, 3.4703729044273343`*^9, {3.4723124398036547`*^9, 3.472312463327655*^9}, {3.472312516078655*^9, 3.472312535965655*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Hsp", "[", "3", "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.470319603131789*^9, 3.470319614650941*^9}, 3.4703197262240973`*^9, 3.4722920511625137`*^9}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", RowBox[{"-", "1"}], "0"}, { RowBox[{"-", "1"}], "0", RowBox[{"-", "1"}]}, {"0", RowBox[{"-", "1"}], "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.470319607674244*^9, 3.4703196154300194`*^9}, { 3.4703197270601807`*^9, 3.4703197353450093`*^9}, 3.4703729106672144`*^9, { 3.472292026743514*^9, 3.4722920518125143`*^9}, 3.4723016483128*^9, { 3.472312540641655*^9, 3.472312543551655*^9}, 3.4723142231870213`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"Emin", "[", "Nl_", "]"}], ":=", RowBox[{ RowBox[{"Sort", "[", RowBox[{"N", "[", RowBox[{"Eigenvalues", "[", RowBox[{"Hsp", "[", "Nl", "]"}], "]"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}], " ", RowBox[{"(*", RowBox[{"Ground", " ", "state", " ", "energy"}], "*)"}], " "}]], "Input", CellChangeTimes->{{3.4703196338858643`*^9, 3.4703196819326687`*^9}, { 3.472312463334655*^9, 3.4723124633386545`*^9}, {3.472313230229655*^9, 3.472313240804655*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"Nl", ",", RowBox[{"Emin", "[", "Nl", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Nl", ",", "1", ",", "20"}], "}"}]}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.4703196857590513`*^9, 3.4703197140648813`*^9}, { 3.4703197464261174`*^9, 3.4703198066211367`*^9}, {3.4722955189598866`*^9, 3.472295523287319*^9}, {3.4723017122104*^9, 3.4723017338943996`*^9}, { 3.4723017756244*^9, 3.4723017828472*^9}, {3.472312463344655*^9, 3.4723124633526545`*^9}, {3.472313247693655*^9, 3.4723132506216545`*^9}}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCwBmIQDQEf7BlQgQNUfD+E5nA4a12fNm/BNyhfwGHFl+mz yx//hPJFHFb5RLyo2vYbypdwKIw5vXLPlT9QvoyDW6/R+ewJf6F8BQcZ3SCn b4L/oHwlh/8hLsJ8+TC+ikN4wNnZWltgfDUH0f0e7ndfwPgaDgy2rJO/CP6H 8rUcMl9GsM4xgvF1HBoYqoz++MD4eg4bYr6fn54E4xs4fF5Xz9BSAuMbOojL NPZ0N8P4Rg6bP7VMcZ0A4xs7xDzRn6IyG8Y3cZC0qe1uWALjw8ILBjjQ+AJo fBE0vgQaXwaNr4DGV0Ljq6Dx1dD4Gmh8LTS+DhpfD41vgMY3ROMbofGN0fgm aPzR9EZuegMA4BzErw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{21, 2}], LineBox[{22, 3}], LineBox[{23, 4}], LineBox[{24, 5}], LineBox[{25, 6}], LineBox[{26, 7}], LineBox[{27, 8}], LineBox[{28, 9}], LineBox[{29, 10}], LineBox[{30, 11}], LineBox[{31, 12}], LineBox[{32, 13}], LineBox[{33, 14}], LineBox[{34, 15}], LineBox[{35, 16}], LineBox[{36, 17}], LineBox[{37, 18}], LineBox[{38, 19}], LineBox[{39, 20}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{5., 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.470319780919566*^9, 3.470319807347209*^9}, 3.4703729107608128`*^9, 3.472292026901514*^9, {3.472295520003991*^9, 3.472295523674358*^9}, 3.4723016485156*^9, 3.4723017209308*^9, 3.472301770726*^9, 3.4723020461907997`*^9, 3.4723132523026547`*^9, 3.4723142233660746`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"(*", RowBox[{ RowBox[{ "For", " ", "large", " ", "lattices", " ", "the", " ", "ground", " ", "state", " ", "energy", " ", "converges", " ", "onto"}], " ", "-", RowBox[{"2", "J"}], " ", "-", " ", RowBox[{ "as", " ", "expected", " ", "from", " ", "the", " ", "Bloch", " ", "wave", " ", "formalism"}]}], "*)"}]], "Input", CellChangeTimes->{{3.472313257834655*^9, 3.472313287073655*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"Nl", "=", "12"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"Hsp", "[", "Nl", "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"ImageSize", "\[Rule]", "200"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ SuperscriptBox[ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], "2"], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"ImageSize", "\[Rule]", "200"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", "Nl"}], "}"}]}], "]"}]}]}], "]"}], "//", "MatrixForm"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.470372916345505*^9, 3.4703730346848297`*^9}, { 3.4703730822277403`*^9, 3.4703731716140213`*^9}, {3.470373258988941*^9, 3.4703733115443306`*^9}, {3.4722955370997005`*^9, 3.4722955441724076`*^9}, {3.4722956341284027`*^9, 3.4722956361676064`*^9}, 3.4722956888908777`*^9, {3.472296130734058*^9, 3.472296130805065*^9}, 3.4723021621768*^9, {3.4723024567047997`*^9, 3.4723024568296003`*^9}, { 3.472312463399655*^9, 3.472312463412655*^9}, {3.4723133237656546`*^9, 3.472313349123655*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7Oe+3JCxgX2HPVTA4Uu89pJ3IcehfA6HlPlF bUVLL0D5Ag4hDvIXjqy4AuWLOHCcKH25s+I6lC/h8IK5tqjq9Q0oXwaNr4Cm XgnNPBU0+9TQ3KPhgOreD/azZoLATrj7UfkcaHwBNL4IGl8CjS+DxldA4yuh 8VXQ+GpofA00/tANfwCd2a4f "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{24, 12}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.941883634852104`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7A+tYS7r4m6yhwo4fHt1vvwH00Ion8NB+7fu rcmBG6F8AYdVy66aPVizC8oXcfgYo7EtyPwglC/hMGMOY82f9MNQvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDqKKDT "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{24, 12}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.941883634852104`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7D/Fay95F3J8P1TAIchB/sKRFVegfA6H18y1 RVWvb0D5Ag4cJ0pf7qy4DuWLOCTPL2orWnoBypdw2PxyQ8YG9h1QvgyMbw/h K8DUQ/lKMPOgfBWYfVC+Gsw9UL6GA9S99jD3M6ACB1QuBxpfAI0vgsaXQOPL oPEV0PhKaHwVNL4aGl8DjT90wx8A1IZ9uw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.7709120513064198`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7D+/Ol/+g2mhPVTAYemyq2YP1uyC8jkc5s5h rPmTfhjKF3D4GKOxLcj8IJQv4qDxW/fW5MCNUL6Ew+M1zGVd3E1QvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwBjt6E/ "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{18, 6}], LineBox[{19, 7}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.7709120513064198`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7FPmF7UVLb1gDxVweM1cW1T1+gaUz+EQ5CB/ 4ciKK1C+gMP0lxsyNrDvgPJFHH7Fay95F3J8P4Qv4cB2ovTlzorrUL4MGl8B Tb0SmnkqaPapoblHwwHVvR9g7oYBB1QuBxpfAI0vgsaXQOPLoPEV0PhKaHwV NL4aGl8DjT90wx8AI9l7Zw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.4970214963422022`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7LV/696aHLjRHirgMHcOY82f9MNQPofD0mVX zR6s2QXlCzjsXMNc1sXdBOWLOPx/db78B9NCKF/C4V2MxrYg84NQvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDcqKDH "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{16, 4}], LineBox[{21, 9}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.4970214963422022`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7IMd5C8cWXFlP1TAgf1E6cudFdehfA6HeS83 ZGxg3wHlCzgkzy9qK1p6wR7CF3F4w1xbVPX6BpQv4fAhXnvJu5DjUL4MjA/V rwBTD+UrwcyD8lVg9kH1q8HcA+VrOEDdaw9zPwMqcEDlcqDxBdD4Imh8CTS+ DBpfAY2vhMZXQeOrofE10PhDN/wB4Xd9Yw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.1361294934623116`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7Jcvu2r2YM0ue6iAw/sYjW1B5gehfA6HI2uY y7q4m6B8AQeN37q3JgduhPJFHObNYaz5k34Yypdw+PDqfPkPpoVQvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDPKKC7 "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{15, 3}], LineBox[{22, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "1.1361294934623116`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7NlPlL7cWXHdHirgkDK/qK1o6QUon8PhU7z2 knchx/dD+AIOr5hri6pe34DyRRzmvdyQsYF9B5Qv4RDsIH/hyIorUP0yaHwF NPVKaOapoNmnhuYeDQdU936AuRsGHFC5HGh8ATS+CBpfAo0vg8ZXQOMrofFV 0PhqaHwNNP7QDX8AVfd9Zw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "0.7092097740850712`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7N/HaGwLMj9oDxVw0P6te2ty4EYon8Ph86vz 5T+YFkL5Ag6z5zDW/Ek/DOWLOBxZw1zWxd0E5Us4LF921ezBml1QvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDcqKDH "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{17, 5}], LineBox[{20, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "0.7092097740850712`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7N8w1xZVvb6xHyrgMOflhowN7DugfA4HjhOl L3dWXLeH8AUcvsRrL3kXchzKF3EIcZC/cGTFFah6CYeU+UVtRUsvQPkyMD5U vQJMPZSvBDMPql4FZh+UrwZzD1S9hgPUvfYw9zOgAgdULgcaXwCNL4LGl0Dj y6DxFdD4Smh8FTS+GhpfA40/dMMfAMf3fXc= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{21, 9}], LineBox[{22, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "0.2410733605106461`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7OfNYaz5k37YHirgcHANc1kXdxOUz+HwMUZj W5D5QShfwOHbq/PlP5gWQvkiDquWXTV7sGYXlC/hoP1b99bkwI1QvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwAAt6Dn "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox[ RowBox[{"-", "0.2410733605106461`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7N8w1xZVvb5hDxVwmPNyQ8YG9h37IVwOB44T pS93VlyH8gUcvsRrL3kXchyqXsQhxEH+wpEVV6B8CYeU+UVtRUsvQNXLoPEV 0NQroZmngmafGpp7NBxQ3fsB5m4YcEDlcqDxBdD4Imh8CTS+DBpfAY2vhMZX QeOrofE10PhDN/wBZ/d9dw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{22, 10}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["0.2410733605106461`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7OfNYaz5k37YHirgcHANc1kXdxOUz+HwMUZj W5D5QShfwOHbq/PlP5gWQvkiDquWXTV7sGYXlC/hoP1b99bkwI1QvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwAAt6Dn "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox["0.2410733605106461`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7NlPlL7cWXF9P1TAIWV+UVvR0gv2EC6Hw6d4 7SXvQo5D+QIOr5hri6pe34CqF3GY93JDxgb2HVB5CYdgB/kLR1ZcgfJlYHyo egWYeihfCWYeVL0KzD6ovBrMPVC+hgPUvfYw9zOgAgdULgcaXwCNL4LGl0Dj y6DxFdD4Smh8FTS+GhpfA40/dMMfADX3fWc= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{16, 4}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{22, 10}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{21, 9}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["0.7092097740850712`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7N/HaGwLMj9oDxVw0P6te2ty4EYon8Ph86vz 5T+YFkL5Ag6z5zDW/Ek/DOWLOBxZw1zWxd0E5Us4LF921ezBml1QvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDcqKDH "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{17, 5}], LineBox[{20, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox["0.7092097740850712`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7IMd5C8cWXHFHirgwH6i9OXOiuv7IVwOh3kv N2RsYN8BlRdwSJ5f1Fa09AKUL+Lwhrm2qOr1Dah6CYcP8dpL3oUch8rLoPEV 0NQroZmngmafGpp7NBxQ3fsB5m4YcEDlcqDxBdD4Imh8CTS+DBpfAY2vhMZX QeOrofE10PhDN/wBH1l7Yw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{17, 5}], LineBox[{20, 8}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.1361294934623116`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7Jcvu2r2YM0ue6iAw/sYjW1B5gehfA6HI2uY y7q4m6B8AQeN37q3JgduhPJFHObNYaz5k34Yypdw+PDqfPkPpoVQvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDPKKC7 "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{15, 3}], LineBox[{22, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.1361294934623116`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7FPmF7UVLb2wHyrg8Jq5tqjq9Q17CJfDIchB /sKRFVeg8gIO019uyNjAvgMqL+LwK157ybuQ41C+hAPbidKXOyuuQ9XLwPhQ eQWYeqi8Esw8KF8FZh9UvRrMPVB5DQeoe+1h7mdABQ6oXA40vgAaXwSNL4HG l0HjK6DxldD4Kmh8NTS+Bhp/6IY/AGX3fWc= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{15, 3}], LineBox[{18, 6}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{19, 7}], LineBox[{22, 10}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.4970214963422022`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7LV/696aHLjRHirgMHcOY82f9MNQPofD0mVX zR6s2QXlCzjsXMNc1sXdBOWLOPx/db78B9NCKF/C4V2MxrYg84NQvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDcqKDH "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{16, 4}], LineBox[{21, 9}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.4970214963422022`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7D/Fay95F3LcHirgEOQgf+HIiiv7IVwOh9fM tUVVr29A5QUcOE6UvtxZcR0qL+KQPL+orWjpBai8hMPmlxsyNrDvgMrLoPEV 0NQroZmngmafGpp7NBxQ3fsB5m4YcEDlcqDxBdD4Imh8CTS+DBpfAY2vhMZX QeOrofE10PhDN/wBtHd9uw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{16, 4}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{21, 9}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{15, 3}], LineBox[{17, 5}], LineBox[{20, 8}], LineBox[{22, 10}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.7709120513064198`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7D+/Ol/+g2mhPVTAYemyq2YP1uyC8jkc5s5h rPmTfhjKF3D4GKOxLcj8IJQv4qDxW/fW5MCNUL6Ew+M1zGVd3E1QvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwBjt6E/ "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{18, 6}], LineBox[{19, 7}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.7709120513064198`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7Oe+3JCxgX3HfqiAw5d47SXvQo7bQ7gcDinz i9qKll6Aygs4hDjIXziy4gpUXsSB40Tpy50V16HyEg4vmGuLql7fgMrLwPhQ eQWYeqi8Esw8qLwKzD6ovBrMPVB5DQeoe+1h7mdABQ6oXA40vgAaXwSNL4HG l0HjK6DxldD4Kmh8NTS+Bhp/6IY/AIp3fWs= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{15, 3}], LineBox[{17, 5}], LineBox[{19, 7}], LineBox[{21, 9}], LineBox[{23, 11}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{16, 4}], LineBox[{18, 6}], LineBox[{20, 8}], LineBox[{22, 10}], LineBox[{24, 12}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.941883634852104`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAWIQDQEf7A+tYS7r4m6yhwo4fHt1vvwH00Ion8NB+7fu rcmBG6F8AYdVy66aPVizC8oXcfgYo7EtyPwglC/hMGMOY82f9MNQvgwaXwFN vRKaeSpo9qmhuUfDAdW9H+yrRda5P6yaAnc/Kp8DjS+AxhdB40ug8WXQ+Apo fCU0vgoaXw2Nr4HGH7rhDwDqKKDT "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 1}], LineBox[{24, 12}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 2}], LineBox[{15, 3}], LineBox[{16, 4}], LineBox[{17, 5}], LineBox[{18, 6}], LineBox[{19, 7}], LineBox[{20, 8}], LineBox[{21, 9}], LineBox[{22, 10}], LineBox[{23, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.02}, Frame->True, ImageSize->200, PlotLabel->FormBox["1.941883634852104`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.472313344959655*^9, 3.4723133509776545`*^9}, 3.4723142236321545`*^9}] }, Open ]], Cell["\<\ Left : Amplitudes Right : Occupations The Occupations in the ground state and the highest excited state are \ identical, but the highest excited state shows fast phase oscillations\ \>", "Text", CellChangeTimes->{{3.472313501392655*^9, 3.4723135614166546`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"Nl", "=", "11"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"Hsp", "[", "Nl", "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"ImageSize", "\[Rule]", "250"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Take", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"Fourier", "[", RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"Ceiling", "[", RowBox[{"Nl", "/", "2"}], "]"}]}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"ImageSize", "\[Rule]", "250"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", "Nl"}], "}"}]}], "]"}]}]}], "]"}], "//", "MatrixForm"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.4703933805222855`*^9, 3.470393390793929*^9}, { 3.4722957065716457`*^9, 3.472295706626652*^9}, {3.4722957962556133`*^9, 3.4722958137363615`*^9}, {3.4722961163976245`*^9, 3.472296116460631*^9}, { 3.4723027134028*^9, 3.4723027140736*^9}, 3.4723027506400003`*^9, { 3.4723124634166546`*^9, 3.472312463432655*^9}, {3.4723135978646545`*^9, 3.4723136385156546`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQBGIQDQEf7I/PvF+ykWe3PVTAwU6Hp2Cvwikon8NB1niC 6/LKS1C+gMM56/q0eQuuQfkiDn2SJxZdtrkJ5UtA9d+C8mXQ5BXQ9Cuhma+C Zr+aA6r7PtjPmgkCO+HuReVzoPEF0PgiaHwJNL4MGl8Bja+ExldB46uh8YdO +AIAABSTkQ== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{13, 2}], LineBox[{14, 3}], LineBox[{15, 4}], LineBox[{16, 5}], LineBox[{17, 6}], LineBox[{18, 7}], LineBox[{19, 8}], LineBox[{20, 9}], LineBox[{21, 10}], LineBox[{22, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.9318516525781366`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.9349726988477374}, {2., 0.24518625077662465`}, {3., 0.04868389419768631}, {4., 0.018825179748605356`}, {5., 0.008165459400181473}, {6., 0.002354774035099013}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {1., 0.9349726988477374}, {2., 0.24518625077662465`}, { 3., 0.04868389419768631}, {4., 0.018825179748605356`}, {5., 0.008165459400181473}, {6., 0.002354774035099013}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 1}], LineBox[{8, 2}], LineBox[{9, 3}], LineBox[{10, 4}], LineBox[{11, 5}], LineBox[{12, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.9318516525781366`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAGIQDQEf7O11eAr2KpzaDxVwOGtdnzZvwTUon8MBIn8L yhdAkxdxQNUv4cCAAmRg8vYQvgJMP5SvBDMfyldBk1dD0//BHtV8BjT7OND4 Amh8EQz3ofIV0PhKaHwVNL4aGn/ohCcAdLdYIw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{13, 2}], LineBox[{14, 3}], LineBox[{15, 4}], LineBox[{16, 5}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{17, 7}], LineBox[{18, 8}], LineBox[{19, 9}], LineBox[{20, 10}], LineBox[{21, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.7320508075688772`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.6999649026201421}, {3., 0.07384237654764655}, {4., 0.0461284485306381}, {5., 0.036810105560509364`}, {6., 0.03337095878980879}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {1., 0.}, {2., 0.6999649026201421}, {3., 0.07384237654764655}, {4., 0.0461284485306381}, {5., 0.036810105560509364`}, {6., 0.03337095878980879}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 2}], LineBox[{8, 3}], LineBox[{9, 4}], LineBox[{10, 5}], LineBox[{11, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{12, 13, 14, 15, 16, 17}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.7320508075688772`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQB2IQDQEf7GWNJ7gur7xkDxVwsNfhKdircAvK53BAlRdw YEABIjD5/RC+BEw/lC+DJq+Apl8JzXwVNPvV0OQ/2KPqZ0AzjwPDfah8CTS+ DIZ7UPkqaHw1NP7QCT8APJ1LJA== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{15, 5}], LineBox[{16, 6}], LineBox[{17, 7}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{13, 2}], LineBox[{14, 3}], LineBox[{18, 9}], LineBox[{19, 10}], LineBox[{20, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.4142135623730951`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.2971691469350306}, {2., 0.6225506234964266}, {3., 0.2510242986476617}, {4., 0.06710249594018826}, {5., 0.026547796077637853`}, {6., 0.007432448427692577}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {1., 0.2971691469350306}, {2., 0.6225506234964266}, { 3., 0.2510242986476617}, {4., 0.06710249594018826}, {5., 0.026547796077637853`}, {6., 0.007432448427692577}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 1}], LineBox[{8, 2}], LineBox[{9, 3}], LineBox[{10, 4}], LineBox[{11, 5}], LineBox[{12, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.4142135623730951`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQA2IQDQEf7M9Y16fNW3BtP1TAAZXP4cCAAgRg8vYQvgga XwJNvQyaeQpofCU09Spo5qmh8T/Yo6pnwHAfKl8Ewz2ofAUM+1H5amj8oRNe ANuHVos= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{13, 2}], LineBox[{16, 7}], LineBox[{17, 8}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 4}], LineBox[{15, 5}], LineBox[{18, 10}], LineBox[{19, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.08800726902511675}, {3., 0.6813561937131163}, {4., 0.12542630267652424`}, {5., 0.08396432025489352}, {6., 0.07229587407691712}, {2., 0.}, {3., 0.}, { 4., 0.}, {5., 0.}, {6., 0.}, {1., 0.}, {2., 0.08800726902511675}, {3., 0.6813561937131163}, {4., 0.12542630267652424`}, {5., 0.08396432025489352}, {6., 0.07229587407691712}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 2}], LineBox[{8, 3}], LineBox[{9, 4}], LineBox[{10, 5}], LineBox[{11, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{12, 13, 14, 15, 16, 17}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "1.`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQBGIQDQEf7PskTyy6bHPTHirgYKvDU7BX4RSUz+EgazzB dXnlpf0QvoDDGev6tHkLrkH5Ig5HZ94v2cizG6peAqr/FpQvgyavgKZfCc18 FTT71RxQ3fcB5k4YcEDlcqDxBdD4Imh8CTS+DBpfAY2vhMZXQeOrofGHTvgC ANmuZVY= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{14, 3}], LineBox[{15, 4}], LineBox[{19, 8}], LineBox[{20, 9}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{13, 2}], LineBox[{16, 5}], LineBox[{17, 6}], LineBox[{18, 7}], LineBox[{21, 10}], LineBox[{22, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "0.5176380902050415`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.16041595422512078`}, {2., 0.19586936984095032`}, {3., 0.6387312078359803}, {4., 0.194102626861533}, {5., 0.05405800132899323}, {6., 0.01388875974619976}, {1., 0.1}, {2., 0.1}, {3., 0.1}, {4., 0.1}, {5., 0.1}, {6., 0.1}, {1., 0.16041595422512078`}, {2., 0.19586936984095032`}, {3., 0.6387312078359803}, {4., 0.194102626861533}, {5., 0.05405800132899323}, {6., 0.01388875974619976}}, {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 5}], LineBox[{12, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 1}], LineBox[{8, 2}], LineBox[{9, 3}], LineBox[{10, 4}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, ImageSize->250, PlotLabel->FormBox[ RowBox[{"-", "0.5176380902050415`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQAWIQDQEf7O11eAr2KtzaDxVwYEABHA5QeXsIXwBNXsQB Vb8EmrwMmn4FNHklNP0qaPJqaPo/2KO7D9096Paj24duPip/6IQHAKSbM0s= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{14, 5}], LineBox[{16, 9}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 3}], LineBox[{15, 7}], LineBox[{17, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["0.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.04122286460102201}, {3., 0.16019710944965915`}, {4., 0.6536657950987838}, {5., 0.17097980188265233`}, {6., 0.12698227129841283`}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {1., 0.}, {2., 0.04122286460102201}, {3., 0.16019710944965915`}, {4., 0.6536657950987838}, {5., 0.17097980188265233`}, {6., 0.12698227129841283`}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 2}], LineBox[{8, 3}], LineBox[{9, 4}], LineBox[{10, 5}], LineBox[{11, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{12, 13, 14, 15, 16, 17}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["0.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQBGIQDQEf7PskTyy6bHPTHirgYKvDU7BX4dR+CJfDQdZ4 guvyyktQvoDDGev6tHkLrkHVizgcnXm/ZCPPbihfAqr/FlS9DJq8App+JTTz VdDsV3NAdd8HmDthwAGVy4HGF0Dji6DxJdD4Mmh8BTS+EhpfBY2vhsYfOuEL ANq9ZlY= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 2}], LineBox[{14, 3}], LineBox[{17, 6}], LineBox[{20, 9}], LineBox[{21, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{15, 4}], LineBox[{16, 5}], LineBox[{18, 7}], LineBox[{19, 8}], LineBox[{22, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["0.5176380902050415`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.09445142301901072}, {2., 0.10370322683557047`}, {3., 0.1483501619598063}, {4., 0.668311837018346}, {5., 0.12471339281064907`}, {6., 0.024149382808923817`}, {1., 0.1}, {2., 0.1}, {3., 0.1}, {4., 0.1}, { 5., 0.1}, {6., 0.1}, {1., 0.09445142301901072}, {2., 0.10370322683557047`}, {3., 0.1483501619598063}, {4., 0.668311837018346}, {5., 0.12471339281064907`}, {6., 0.024149382808923817`}}, {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 1}], LineBox[{12, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 2}], LineBox[{9, 3}], LineBox[{10, 4}], LineBox[{11, 5}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, ImageSize->250, PlotLabel->FormBox["0.5176380902050415`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQA2IQDQEf7M9Y16fNW3BtP1TAAcq3h3A5HBhQgIADqnoR NPUSaOpl0NQroKlXQlOvgqZeDU39B3tU9QwY7kPli2C4B5WvgGE/Kl8NjT90 wgsAm4dWiw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{14, 4}], LineBox[{16, 7}], LineBox[{18, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 2}], LineBox[{15, 5}], LineBox[{17, 8}], LineBox[{19, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.022391584241534576`}, {3., 0.06295778850875079}, {4., 0.22523488234728936`}, {5., 0.6261567670797906}, {6., 0.22963424099081794`}, {2., 0.}, {3., 0.}, { 4., 0.}, {5., 0.}, {6., 0.}, {1., 0.}, {2., 0.022391584241534576`}, { 3., 0.06295778850875079}, {4., 0.22523488234728936`}, {5., 0.6261567670797906}, {6., 0.22963424099081794`}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 2}], LineBox[{8, 3}], LineBox[{9, 4}], LineBox[{10, 5}], LineBox[{11, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{12, 13, 14, 15, 16, 17}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQB2IQDQEf7GWNJ7gur7xkDxVwsNfhKdircGs/hMvhgCov 4MCAAkRg8lD1EjD9UPUyaPIKaPqV0MxXQbNfDU3+gz2qfgY08zgw3IfKl0Dj y2C4B5WvgsZXQ+MPnfADAC2sTCQ= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 2}], LineBox[{15, 5}], LineBox[{17, 7}], LineBox[{19, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{14, 3}], LineBox[{16, 6}], LineBox[{18, 9}], LineBox[{20, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.4142135623730951`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.050986164976365114`}, {2., 0.05393650503718011}, {3., 0.06522966583716894}, {4., 0.10091912869243082`}, {5., 0.692056868706636}, {6., 0.04907921708395369}, {1., 0.1}, {2., 0.1}, {3., 0.1}, {4., 0.1}, {5., 0.1}, {6., 0.1}, {1., 0.050986164976365114`}, {2., 0.05393650503718011}, {3., 0.06522966583716894}, {4., 0.10091912869243082`}, {5., 0.692056868706636}, {6., 0.04907921708395369}}, {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 1}], LineBox[{8, 2}], LineBox[{9, 3}], LineBox[{12, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 4}], LineBox[{11, 5}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.4142135623730951`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQAGIQDQEf7O11eAr2KpzaDxVwOGtdnzZvwTV7CJfDASJ/ CyovgCYv4oCqX8KBAQXIwOSh6hVg+qHqlWDmQ+VV0OTV0PR/sEc1nwHNPg40 vgAaXwTDfah8BTS+EhpfBY2vhsYfOuEJALSoWCM= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{14, 3}], LineBox[{16, 5}], LineBox[{18, 8}], LineBox[{20, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 2}], LineBox[{15, 4}], LineBox[{17, 7}], LineBox[{19, 9}], LineBox[{21, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.7320508075688772`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 8.368620923398063*^-18}, {2., 0.010156184714542282`}, {3., 0.025966203123118505`}, {4., 0.06427040473601328}, {5., 0.2651200095072257}, {6., 0.6517693639941745}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {1., 8.368620923398063*^-18}, {2., 0.010156184714542282`}, {3., 0.025966203123118505`}, {4., 0.06427040473601328}, {5., 0.2651200095072257}, {6., 0.6517693639941745}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 1}], LineBox[{8, 2}], LineBox[{9, 3}], LineBox[{10, 4}], LineBox[{11, 5}], LineBox[{12, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.7320508075688772`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}, { GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQBGIQDQEf7I/PvF+ykWe3PVTAwU6Hp2Cvwqn9EC6Hg6zx BNfllZeg8gIO56zr0+YtuAaVF3Hokzyx6LLNTai8BFT/Lai8DJq8App+JTTz VdDsV3NAdd8HmDthwAGVy4HGF0Dji6DxJdD4Mmh8BTS+EhpfBY2vhsYfOuEL APFtZmw= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{13, 2}], LineBox[{15, 4}], LineBox[{17, 6}], LineBox[{19, 8}], LineBox[{21, 10}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 1}], LineBox[{14, 3}], LineBox[{16, 5}], LineBox[{18, 7}], LineBox[{20, 9}], LineBox[{22, 11}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.9318516525781366`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], GraphicsBox[ GraphicsComplexBox[{{1., 0.01620530221918553}, {2., 0.01691471964550505}, {3., 0.01940217028732201}, {4., 0.025330926880130916`}, {5., 0.04254565098975162}, {6., 0.7048080262473604}, {1., 0.1}, {2., 0.1}, {3., 0.1}, {4., 0.1}, {5., 0.1}, {6., 0.1}, {1., 0.01620530221918553}, {2., 0.01691471964550505}, {3., 0.01940217028732201}, {4., 0.025330926880130916`}, {5., 0.04254565098975162}, {6., 0.7048080262473604}}, {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{7, 1}], LineBox[{8, 2}], LineBox[{9, 3}], LineBox[{10, 4}], LineBox[{11, 5}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{12, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, ImageSize->250, PlotLabel->FormBox["1.9318516525781366`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{ 3.470393392979385*^9, 3.4722920279185143`*^9, 3.472295586617652*^9, 3.472295708961885*^9, 3.472295816784666*^9, 3.472296117484733*^9, 3.472301650762*^9, 3.4723027188316*^9, 3.4723027630888*^9, { 3.4723136055486546`*^9, 3.4723136395526547`*^9}, 3.472314224085291*^9}] }, Open ]], Cell["\<\ Left : Amplitudes Right : The Fourier transform of the amplitudes \ corresponds to the quasimomentum distribution\ \>", "Text", CellChangeTimes->{{3.472313712147908*^9, 3.4723137706179695`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Many particles - multiple wells", "Section", CellChangeTimes->{{3.4703198131447887`*^9, 3.4703198205795317`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"NNN", "[", RowBox[{"Nl_", ",", "Na_"}], "]"}], ":=", RowBox[{"Binomial", "[", RowBox[{ RowBox[{"Na", "+", "Nl", "-", "1"}], ",", "Na"}], "]"}]}], ";"}]], "Input", CellChangeTimes->{{3.4703203935618243`*^9, 3.470320450383506*^9}, { 3.472295892678255*^9, 3.4722959432093077`*^9}, {3.4722959954835343`*^9, 3.472295998050791*^9}, 3.472312464413655*^9, {3.472313677632211*^9, 3.472313685414878*^9}, 3.472313786730631*^9}], Cell["\<\ The number of possibile ways to distribute Na bosonic atoms over Nl lattice \ sites. \"Urnenmodell: Mit zur\[UDoubleDot]cklegen; ohne Ber\[UDoubleDot]cksichtigung \ der Reihenfolge\"\ \>", "Text", CellChangeTimes->{{3.4723136973770514`*^9, 3.4723136975291424`*^9}, { 3.4723137908190823`*^9, 3.4723138222849507`*^9}, {3.472313888696774*^9, 3.472313895635935*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NNN", "[", RowBox[{"500", ",", "2"}], "]"}]], "Input", CellChangeTimes->{{3.470320453957864*^9, 3.470320472055673*^9}, { 3.4723032019948*^9, 3.4723032457372*^9}}], Cell[BoxData["125250"], "Output", CellChangeTimes->{{3.470320462903758*^9, 3.4703204724477124`*^9}, 3.4722959545734434`*^9, {3.4723032068152*^9, 3.4723032265648003`*^9}, 3.4723032608068*^9, 3.4723142275343246`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"Nl", ",", RowBox[{"NNN", "[", RowBox[{"Nl", ",", "5"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Nl", ",", "1", ",", "10"}], "}"}]}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470320487706238*^9, 3.4703204932107887`*^9}, { 3.4722960022842145`*^9, 3.4722960060125875`*^9}}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQA2IQDQEf7FFpBgcIJQGlOaC0KZQWgNI+UFoEQjfEo+pr yIfyZSD0gxooXwFCH+iA8pUgtMwUKF8FQnvMd0BzFww4oHI50PgCaHwRNL4E Gl8Gja+AxldC46ug8Qdv+AEAhvYijQ== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 1}], LineBox[{12, 2}], LineBox[{13, 3}], LineBox[{14, 4}], LineBox[{15, 5}], LineBox[{16, 6}], LineBox[{17, 7}], LineBox[{18, 8}], LineBox[{19, 9}], LineBox[{20, 10}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{21, 22, 23, 24, 25, 26, 27, 28, 29, 30}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{2., 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.470320500014469*^9, 3.472295954627449*^9, 3.472296007480734*^9, 3.4723032809152*^9, 3.472314227578338*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"Nl", ",", RowBox[{"NNN", "[", RowBox[{"Nl", ",", "25"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Nl", ",", "1", ",", "10"}], "}"}]}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{ 3.4703205125157185`*^9, {3.4723124651026545`*^9, 3.472312465104655*^9}}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQA2IQDQEf7FFpBgcIZQWlOSD0h1IoXwBCz1gJ5YuA6QOG 16F8CTAdkMroCOHLgPlGFWpQvgKY/2GtJ5SvBOI3xFdnQfkqIP6BvUydjmju ggEHVC4HGl8AjS+CxpdA48ug8RXQ+EpofBU0/uANPwC2Dy0T "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 1}], LineBox[{12, 2}], LineBox[{13, 3}], LineBox[{14, 4}], LineBox[{15, 5}], LineBox[{16, 6}], LineBox[{17, 7}], LineBox[{18, 8}], LineBox[{19, 9}], LineBox[{20, 10}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{21, 22, 23, 24, 25, 26, 27, 28, 29, 30}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{2., 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.4703205133258*^9, 3.4722959546604524`*^9, 3.472303304908*^9, 3.4723142276043463`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NNN", "[", RowBox[{"20", ",", "20"}], "]"}]], "Input", CellChangeTimes->{{3.4703205250669737`*^9, 3.4703205473472013`*^9}, { 3.4723034479132*^9, 3.4723034521876*^9}, {3.47231390806839*^9, 3.4723139103087335`*^9}}], Cell[BoxData["68923264410"], "Output", CellChangeTimes->{{3.470320526081075*^9, 3.470320548050272*^9}, 3.472295954686455*^9, 3.472303453108*^9, 3.4723139115014486`*^9, 3.4723142276313543`*^9}] }, Open ]], Cell["\<\ This shows that it is impossible to use exact numerical methods in order to \ srudy large systems, as the number of basis states diverges too fast!\ \>", "Text", CellChangeTimes->{{3.472313915057581*^9, 3.4723139708623466`*^9}}] }, Open ]] }, Open ]] }, WindowSize->{1446, 960}, WindowMargins->{{207, Automatic}, {Automatic, 43}}, FrontEndVersion->"7.0 for Microsoft Windows (64-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 207, 2, 83, "Title"], Cell[777, 26, 117, 1, 28, "Subsubtitle"], Cell[CellGroupData[{ Cell[919, 31, 186, 2, 71, "Section"], Cell[1108, 35, 278, 8, 31, "Input"], Cell[CellGroupData[{ Cell[1411, 47, 160, 2, 36, "Subsection"], Cell[CellGroupData[{ Cell[1596, 53, 116, 1, 27, "Subsubsection"], Cell[1715, 56, 783, 25, 33, "Input"], Cell[CellGroupData[{ Cell[2523, 85, 902, 20, 31, "Input"], Cell[3428, 107, 13849, 231, 243, "Output"] }, Open ]], Cell[17292, 341, 481, 14, 31, "Input"], Cell[CellGroupData[{ Cell[17798, 359, 365, 9, 31, "Input"], Cell[18166, 370, 6181, 107, 247, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[24396, 483, 160, 2, 27, "Subsubsection"], Cell[24559, 487, 1117, 28, 72, "Input"], Cell[CellGroupData[{ Cell[25701, 519, 128, 2, 31, "Input"], Cell[25832, 523, 1829, 56, 206, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27698, 584, 648, 17, 52, "Input"], Cell[28349, 603, 1315, 29, 161, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[29713, 638, 104, 1, 27, "Subsubsection"], Cell[29820, 641, 265, 8, 31, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[30134, 655, 105, 1, 36, "Subsection"], Cell[30242, 658, 739, 21, 31, "Input"], Cell[30984, 681, 371, 10, 31, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[31392, 696, 161, 2, 36, "Subsection"], Cell[CellGroupData[{ Cell[31578, 702, 106, 1, 27, "Subsubsection"], Cell[CellGroupData[{ Cell[31709, 707, 335, 9, 31, "Input"], Cell[32047, 718, 65153, 1081, 241, "Output"] }, Open ]], Cell[97215, 1802, 367, 8, 31, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[97619, 1815, 177, 2, 27, "Subsubsection"], Cell[CellGroupData[{ Cell[97821, 1821, 1514, 38, 72, "Input"], Cell[99338, 1861, 1050, 22, 255, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[100437, 1889, 176, 3, 27, "Subsubsection"], Cell[100616, 1894, 1071, 27, 52, "Input"], Cell[CellGroupData[{ Cell[101712, 1925, 1776, 43, 76, "Input"], Cell[103491, 1970, 1788, 33, 255, "Output"] }, Open ]], Cell[105294, 2006, 798, 21, 53, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[106129, 2032, 122, 1, 27, "Subsubsection"], Cell[CellGroupData[{ Cell[106276, 2037, 3025, 71, 120, "Input"], Cell[109304, 2110, 17722, 386, 1343, "Output"] }, Open ]], Cell[127041, 2499, 230, 5, 31, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[127320, 2510, 157, 2, 36, "Subsection"], Cell[CellGroupData[{ Cell[127502, 2516, 382, 10, 31, "Input"], Cell[127887, 2528, 16492, 282, 242, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[144416, 2815, 337, 9, 31, "Input"], Cell[144756, 2826, 14738, 255, 242, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[159531, 3086, 147, 3, 31, "Input"], Cell[159681, 3091, 359, 7, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[160077, 3103, 432, 10, 31, "Input"], Cell[160512, 3115, 16316, 278, 261, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[176865, 3398, 1967, 47, 120, "Input"], Cell[178835, 3447, 8796, 181, 305, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[187668, 3633, 1782, 44, 112, "Input"], Cell[189453, 3679, 8445, 175, 315, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[197935, 3859, 1855, 45, 112, "Input"], Cell[199793, 3906, 8634, 178, 320, "Output"] }, Open ]], Cell[208442, 4087, 383, 8, 47, "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[208874, 4101, 170, 2, 71, "Section"], Cell[209047, 4105, 800, 21, 31, "Input"], Cell[CellGroupData[{ Cell[209872, 4130, 207, 4, 31, "Input"], Cell[210082, 4136, 997, 26, 71, "Output"] }, Open ]], Cell[211094, 4165, 531, 13, 31, "Input"], Cell[CellGroupData[{ Cell[211650, 4182, 960, 21, 31, "Input"], Cell[212613, 4205, 1588, 30, 239, "Output"] }, Open ]], Cell[214216, 4238, 438, 10, 31, "Input"], Cell[CellGroupData[{ Cell[214679, 4252, 3023, 69, 141, "Input"], Cell[217705, 4323, 27705, 569, 1793, "Output"] }, Open ]], Cell[245425, 4895, 273, 5, 47, "Text"], Cell[CellGroupData[{ Cell[245723, 4904, 3133, 73, 152, "Input"], Cell[248859, 4979, 24235, 504, 2016, "Output"] }, Open ]], Cell[273109, 5486, 206, 4, 29, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[273352, 5495, 120, 1, 71, "Section"], Cell[273475, 5498, 497, 12, 31, "Input"], Cell[273975, 5512, 378, 8, 47, "Text"], Cell[CellGroupData[{ Cell[274378, 5524, 192, 4, 31, "Input"], Cell[274573, 5530, 223, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[274833, 5538, 745, 19, 31, "Input"], Cell[275581, 5559, 945, 19, 239, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[276563, 5583, 720, 19, 31, "Input"], Cell[277286, 5604, 940, 19, 232, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[278263, 5628, 246, 5, 31, "Input"], Cell[278512, 5635, 201, 3, 30, "Output"] }, Open ]], Cell[278728, 5641, 239, 4, 29, "Text"] }, Open ]] }, Open ]] } ] *) *^9, 3.4703101510085716`*^9}, { 3.4703101886263328`*^9, 3.4703102359570656`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"interaction", "[", RowBox[{"5", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470310902407045*^9, 3.4703109400542793`*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwt2Hk8VO37B/CZOWfGEoWptHBmlOwJ45FKzYf2UiFa9DyEFFmzlEoRbSrx lKJEkhaRSkVKZLKLelJSqSwhQlL28Lu/r9fvr3m9X+eeOffc13Vf132OmrOP jSuHxWIpsVms/30mHHTmGW7bv8jJqaFrbEyEwmqh5UbhZvH8/GXm/D8ijBXn hQuF7mIbbrCh5oAICc8iBVzhXrHlqg3frbpF8FwY6NUviBBvzC4rTKsXoXrY LaZbcEFcp5o+PqRABKmPjZqdglTxaRXH0fhwEa6UX971XZAjvlR/YM0dGREy 7kR89NQvF4fumCKqkDHCDvF/Fzr8qsVWroUO62cZwrtZu+lBxnvx9crNpzXW GUBW7bDmF9N6sVb+lfEJTfo4rVChc2Vrk9iirP6W8pbZcP5om0+9aBE3Rixr MijVxa6iw84+mu3ivD3Rk1zW6+Cer9z6KSs7xfXZ5bN7x2njyn6PdoON3eLg aTZTlfI1EXb5j/Xvjp9iTvHZTNUEDbCq65G775d4yqk1bx1jZkEjYHuQrU6v 2C/j1bvBE+r42hu7YdzTPrH34GJe7Y2ZWNW888CZXQNiTu7X1azSGVj7NVqX YYbEbenLB+s5M9D+3Dm09PawuGSqhfciRzXoK9aoLnYcEattXZpT9VyIlsiW sHOuI+LdsxfXPiwQIkG2v7XVY0SsLz1skpgvhBw9JfNU0Ii4sDnuvt8TIdr7 Ni+r+XdEHGkemapzX4hrdZ+83QtHxLH7Nx2vSRZC5WZzfpT2qDh0MEiRCRdC VtzrVPdrVHxXpdHac7kQQeZa0llDo2Lfr3ELDywl91+8JSOKPSYu3JSVFLVY CMmKgiGLCWNi7eWzKh+JhdhnE3k2VWdMXD+/Ok/FVIjvrrOKdjuNieUO+nB1 tYV4ccpOS/HlmNjWP1XgJCfE/KjjVe1vx8RnKv8aSJIV4ua/TwIK68bE295o rWiUFuLwebWCPe1j4uetFmvduUIwr/r0fnBYaFx1ukVxRICa95IiO4YFpUGB uWqjAMs77ftn2LFgJVqmsCNDgMSJ4dUhm1gIS0oxWJ8mwO8FaXfqtrAQLJ2j bnFTgKQTwzvOO7NQWEod10oWYEjzUq2MLwsZsmoLlM8LkO78Kaf7BLnf2X3r gw8KoFDrGJz3jIXyJ6mWrtYCbB87tml6IQsth0qa0tYKkKtx1ziohFy3iF/b u1oA90BWp2EVC98ebLscvUwAidKVf659ZOGgfcjstgUCBKxpXHSqjwVeWvWw mqYAtZJtbHs9NuKcBrZmjjHoNv8w7cAcNs7MD1YMHmEgVbDOOMmIjd/mH+au GGZgkj9/R4spGz0f1Vta+xjEPFGo9FvKxgez36VLuhise5Abd9KBDdvM/TcC PjEovjbR4Gk0Gx0es0vTnzL4rH5iZf1ZNlhK/aKiJwx6r445U7FsHGy5OKk+ h4F6cvu5lQlsPJi2a75qFoOwxGfDb1PZkL27UfZhBoNFsZ4lXRI2nE/LP7dP YvDweKGDsJeMn6oSd/AIg5urKqYcG2DDQNvG+3k4g4tyr193DpP5+3dqjQtj EBr9ZdkTDgdWT9avvnqQgWXckP4GBQ7sFb8s6dvDoPGGwdhJXQ4kH7plNT0Y vHWfm9Ojz8HdxH2aF90ZlOou8t9sxEFjgruWghuD23dWt2rM40C4ds872pVB UPb2lwXLOOgItG5XcGQwvuTS5X4nDmoaWU331zNgR1zd7ODKgdGWz0vtbBj8 XnWLX+RGro9Xixy0YvC+KvvYGR8OejRrSletZZBS89pn9gEOQtXGfk9YyWB+ izRc4sjvG1oKZ4kZbOcG1ldVcSBd+lqybzaDaYKyd8P/cWC76XNOhB6DKlPV l1pvOXjmssEkXpfEz7PoadhHDrq/n8wv0mbAq54Ub/KNg8wCOf48DQbXkrLs EtkUCsNc8+IEDDY9ll1TQVNoLzSVe8UwkHvjsGRAioJBWNAXGeIAKSmRzXgK St4LJx9RYbDEe6MCbzoFs3GfCi9MZfB1wUC5lzEFlS3+GmYTGcTZWUouziVe N74ink/W3ycpp2Q+GZ83qXdEicGD5BU31cwpvJbf+b5MkcFhmQtH3q6h4Oyn 1RQygYHpzM5gjjUFK7Hm/V/jGXSYmQfMsaXw97Ez0juJbX3bnCPsKbw4nrHY QZ7k07t5WLiDgoL1n6Ft4xjUdkfO3bmTQkefQ1+HLINTso36sV4Uvirr79lD /HvhCdWf/hT0KxRlYmQYFKZ8GEoJpaDR3+X1XYrEN0+/579wCl2BD2OOEevV hrWNHqVQ7fMNGsQx43RrN0VS6H9zVtuDx8DFb/9DuYsUkrexzPhcsv5Gnx9q J1D4aXZ4ShHNQLYHWcuSKAx02TvtJb67i5cdep2CXj3LtI1iEG7onp2QSmGz 4FVRCvGGnxXZj9MpLDLtyXcm/uP776PfmRTm9OsPNnMYvDT4/Ugxi8KChJWm acTJ3Rty9HMojKpkN/kRr/RVeeyWTyE99USIDLGKQcjjIxIKsVndPrVssv9/ NDxOLqIwLyH1RSrxeZ8bT+oqKKT08yvWE7vPkc0drKLg5VHkqUds9sMzd/Jr sh6PyvZJESvceZkrekvWq17Y+5XFoMnb6KlVLYXJDeUfC4mz9M899fpIIe9J if4N4hNd/U9PfKag6qvcdZL4nwz7vBsNFIxHc6b6Ext4P80r/EqBs/3Ovb+J KX1hfkMrhYgb/Q9XENd0huWPtlMolpzRmEucers5f3oXhdzsUEqLONhrxTPT nxTcjxZYTideNzvtmd1vClX6dhxF4hmd8gV+/SS/7y5QlyHuS/ctiBoi85ML zKSIyzyrC9JHKKyyYN9mEV/SM5GUsWhEWtfz/2ffjjhJC0Xj+HylVjbx4vRh CSVFY8HIeQ0e8WRPh+dCWRrXLni/liNu0y14vlCeRsmEC+2TiHO/zyy0V6CR 5DjZR404Ku1o4R4+DcOIFsc5xM4ebYUxk2nsOyXzVEz8l65l0b2pxO4hR22I pb9nFFWp0DASrsjdQVx3S7H4u4BG8l0XhxDiOzsDiqVn0iib9trzAnGYzrvi WRo0bjqcbX1IvKF9XomFNg1x8I2qN8R/3MdKgufQOLuktGEqiedLbefSC0Y0 rH+8kQdxclthadZfNIr9ja+7Ea90P1HWvYDGO5mO6QXEKtqdZfJiGv7Tlwx2 /y+fvq0r17Eg/5f3w2ImybfzbpMqtq2gcW7nwulRxO5aQRWHVtNQaKpPLSU2 +/ahInEtDYu/3qXQJL8bdyS9qLWlUbk990s48ZwdulWWTjRCR93cL5P98tld 4HN7Gw2vkYjRHuJTnnyF8W40PO499lpJ9lvbrmHrl940Lpiu/jBKfDW44q11 MA3Jc62Ok2S/2oTk784MoWHiUWLdR8wKu6/MD6eRWxL4r4s0ycdj8ZvfRNAY usy+vIzUA+UzHp82xNJYUvm2R5/Uk+IYx4PZF2lAtUfrLnFA7HrBlEQaa2cw 84zlGPx3aYHT+xQaiauvtS4h9ejkjXHNWzJp8Kb7HjhO6tlYblrH1koasrf7 T8aR+piRfzmy4BWNyWsnuCyfxOBvyVn9GW9oGKeYTBwkzinZ79v0gcTX5wHt qszA//Xq367faFiGezKO0xi0tn4f3klx8SqhyrhOSNa7/culCh4XXVEN6Y/U SH3urF6oJ8uFylx6LHYGgys9T0I6Fbi4lRJk6KjOYMvIScqX4SLmj+rLCVok /kp64wLncRF32b5zcA7pv15ebfFmXCTbtmr1GJD5lmSUSMRclE9bUN9hyOB0 sOFhhWVc7P4wV9ImIvW9xWQkzYaLRZpH17NNGZTnmP9o9ODiTF9g2g2QfjYx vFLGh4ujT/2vlpgzuOVdmGbgx8XFc6bK7RYMImYudzsYROa7V9nPZCmDFZGW DVOPkPnJ6/R2kH5YtHVjtVUiFxaeyQb/kf5q/CTu3p4rXMxYqtg8xY70z0kf ohJTiOcsn+SygfST8r8tO25xEWwi3Ta6iYGFsXPRsWwukpS+/GPrwOCZlFd2 3isu0ln1wbtJv3+SERavR/Hw4r5+dOwh0i8t7abF8njYqjUwZEXOF9ZtmhfY sjzo65y1kifnj9aZledrFHgIfrsw9/RxBvwLymdCGR6+lrueexDFwCM8/fib eTzUGbDWnUpkMH1TTWCwLw+ebQ5fPPJIP++9+bvFnwdfrn1K2DMG987s97fe w0NGhobtJQmD5ZXCXRoHefh80zigtpjE38LD89VJHnhmM7P8XzKo0GO5qN/g 4eCnVeYmDQz2s3WsXnziQUG+MOA7T4CWJeNqNRp4OJX9eJKtjABWxzscD30l 1jp4NH+cAOoT7viYfOeBcfB4l6ggwAsV46ikAR6OK38xCZkmAGO6qCqALwW/ 57odxfrkfOltY6m6UgopY5sN/DYLIFu3b4X3AykEycgKTLMFMNmTKh+VLYUB nS5a8FgAJ6Xa13ceS8HiJO8f6acCPFrx1z8/n0nBWPqNS6OEnG8f/tgVUCmF S78aKu5XCVBwelv8vhYpbI8u475oEZDng7VdR6dIY6TbRcGdnOebr6vFXA6W xlG/Z3unWQjRcbhhkAqVxqN3UWacJUL0OF9xdAuXRvyhWJ/v5HmCJVDTNTwh jd1X12lIVgoxLVYokcRKY7/ApSbUWgirY4Lu5kxpFA1MNl/sJETuDlVLvTZp bDTIRN0hIWK0ptI5djLwu5/1zaFEiOiL20uchLIomcr6cmKTGuxj/qmSa5WF 9cJYFZshNQwsuTZ4OW8cdhpNnZKWPwNNzRZBkmNyuNmn62JxaiaSFxpOr3SS h4NLcdTfoeq4fSRQccfs8aDlZ6eb752FY3Yuq6ne8Ui/qMbvCNXAX3VXUo9V TgDvpnJm+wNNxGnH365crQDv2AlnuW1aCHkWGbc6RwHS2p8cd67RwZrpdtfK 1RWRZ7DtlrJEF+beJVsUIxRhJoq5PsloNi6rOKu/6FUE3vnFrnqnD/XnN86v 3aKE3F8mlnfmGyB6tkTndZ4SLG/S7R4TDLH9F/1fmQ4fBhPNf+qwjeB8r0cY EcWHc/Ct91SnETzD1v9Z9S8f5WcfBs39aYTA9Q/eyZ3lIy7Y6ZNHrxGO9wae jj7Ph5skvr9mxAgZ8waHYxP4qGcu+mSNF2GwYKzmehofKtPzvC4aiBD9Wi6y sISPD8KryX0BIly86uV2tIwPddfSXou9IlwNqFq8ooKPV/tOj48+IELW5Oih iio+tk0bidY7KkKdPd+t+i0ff+tse+8dK4Jm09TFjU18XIrcHDTlsQgGD/Yx Kc182Hw7OWtXngjzj3wcdG3lw2+iY1y5RARLzYS7be18fK1vrQqpEMHPQ8j8 /Em+vyo85FedCMFmhwYzf/Fx2iB3s02DCEfkG98E9JLxrecG7zWLEHfn6smB AT6Ky3VP+HeJkBxK73g8xIdtX+u+tz0ipFm7WgT/4WPZryWGpv0iPJhRrLpo lI/EAovb8cMi5P3SGBwb42Pr/78P+T8Zxy0D "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 8.}, Frame->True, PlotRange->{{0, 5}, {7.500000296179121, 19.999998979591854`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.4703115491765947`*^9}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Build Matrices", "Section", CellChangeTimes->{{3.470310250758402*^9, 3.4703102631794014`*^9}, { 3.4703113498364067`*^9, 3.4703113512034063`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"NAtom", "=", "6"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"JJ", "=", RowBox[{"Table", "[", RowBox[{"0", ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "NAtom"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "NAtom"}], "}"}]}], "]"}]}], ";", " ", RowBox[{"(*", RowBox[{"Tunnel", " ", "Matrix"}], "*)"}], "\[IndentingNewLine]", RowBox[{"UU", "=", RowBox[{"Table", "[", RowBox[{"0", ",", RowBox[{"{", RowBox[{"i", ",", "0", ",", "NAtom"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "0", ",", "NAtom"}], "}"}]}], "]"}]}], ";", " ", RowBox[{"(*", RowBox[{"Interaction", " ", "Matrix"}], "*)"}]}]}], "Input", CellChangeTimes->{{3.4703106422237267`*^9, 3.470310750292258*^9}, { 3.470310964275407*^9, 3.470310965874407*^9}, {3.470311288544407*^9, 3.470311330006407*^9}, 3.4703150568436375`*^9}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "1"}], ",", RowBox[{"i", "\[LessEqual]", RowBox[{"NAtom", "+", "1"}]}], ",", RowBox[{"i", "++"}], ",", RowBox[{ RowBox[{"UU", "[", RowBox[{"[", RowBox[{"i", ",", "i"}], "]"}], "]"}], "=", RowBox[{"interaction", "[", RowBox[{"NAtom", ",", RowBox[{"i", "-", "1"}]}], "]"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"UU", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.4703107555807285`*^9, 3.47031085336395*^9}, { 3.4703109680754066`*^9, 3.4703109924094067`*^9}, {3.4703113419824066`*^9, 3.4703113740294065`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"30", "0", "0", "0", "0", "0", "0"}, {"0", "20", "0", "0", "0", "0", "0"}, {"0", "0", "14", "0", "0", "0", "0"}, {"0", "0", "0", "12", "0", "0", "0"}, {"0", "0", "0", "0", "14", "0", "0"}, {"0", "0", "0", "0", "0", "20", "0"}, {"0", "0", "0", "0", "0", "0", "30"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.4703115821898956`*^9, 3.470315060578637*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"For", "[", RowBox[{ RowBox[{"i", "=", "1"}], ",", RowBox[{"i", "\[LessEqual]", "NAtom"}], ",", RowBox[{"i", "++"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"JJ", "[", RowBox[{"[", RowBox[{"i", ",", RowBox[{"i", "+", "1"}]}], "]"}], "]"}], "=", RowBox[{"tunnel", "[", RowBox[{"NAtom", ",", RowBox[{"i", "-", "1"}], ",", "i"}], "]"}]}], ",", RowBox[{ RowBox[{"JJ", "[", RowBox[{"[", RowBox[{ RowBox[{"i", "+", "1"}], ",", "i"}], "]"}], "]"}], "=", RowBox[{"tunnel", "[", RowBox[{"NAtom", ",", RowBox[{"i", "-", "1"}], ",", "i"}], "]"}]}]}], "}"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"JJ", "//", "MatrixForm"}]}], "Input", CellChangeTimes->{{3.4703110008044066`*^9, 3.4703111321154065`*^9}, { 3.4703111804244065`*^9, 3.4703112070224066`*^9}, {3.4703113886284065`*^9, 3.4703114075004287`*^9}, {3.470311586604337*^9, 3.4703115921798944`*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", FractionBox["1", RowBox[{"120", " ", SqrtBox["6"]}]], "0", "0", "0", "0", "0"}, { FractionBox["1", RowBox[{"120", " ", SqrtBox["6"]}]], "0", FractionBox["1", RowBox[{"24", " ", SqrtBox["10"]}]], "0", "0", "0", "0"}, {"0", FractionBox["1", RowBox[{"24", " ", SqrtBox["10"]}]], "0", FractionBox["1", RowBox[{"24", " ", SqrtBox["3"]}]], "0", "0", "0"}, {"0", "0", FractionBox["1", RowBox[{"24", " ", SqrtBox["3"]}]], "0", FractionBox["1", RowBox[{"24", " ", SqrtBox["3"]}]], "0", "0"}, {"0", "0", "0", FractionBox["1", RowBox[{"24", " ", SqrtBox["3"]}]], "0", FractionBox["1", RowBox[{"24", " ", SqrtBox["10"]}]], "0"}, {"0", "0", "0", "0", FractionBox["1", RowBox[{"24", " ", SqrtBox["10"]}]], "0", FractionBox["1", RowBox[{"120", " ", SqrtBox["6"]}]]}, {"0", "0", "0", "0", "0", FractionBox["1", RowBox[{"120", " ", SqrtBox["6"]}]], "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.470311582211898*^9, 3.470311593243001*^9}, 3.470315060601637*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Solve Hamiltonian", "Section", CellChangeTimes->{{3.4703112507764063`*^9, 3.4703112580334063`*^9}, { 3.4703115974504213`*^9, 3.470311598201497*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"H", "[", RowBox[{"J_", ",", "U_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{"-", "J"}], "*", "JJ"}], "+", RowBox[{"U", "*", "UU"}]}]}]], "Input", CellChangeTimes->{{3.4703114324659247`*^9, 3.470311457260404*^9}}], Cell[CellGroupData[{ Cell["Plot Eigenenergies", "Subsection", CellChangeTimes->{{3.4703116334230185`*^9, 3.4703116406437407`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Energy", "[", RowBox[{"J_", ",", "U_"}], "]"}], ":=", RowBox[{"Sort", "[", RowBox[{"N", "[", RowBox[{"Eigenvalues", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], StyleBox["]", "Subsubsection"]}], StyleBox["]", "Subsubsection"]}]}]], "Input", CellChangeTimes->{{3.4703116528769636`*^9, 3.4703116824379196`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Energy", "[", RowBox[{"J", ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"J", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{3.470311767115405*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwV0vs3lAkYwPGxg0pKyrpmLl4lw3RxdE4U77OxmzRsijLTVmsUKte2KZvk MqwQSSqUNG67KroNSyuPW7mPa/OWGSeS07IqZWcxaW37w/d8/oEvWxi26/BX NBrN40v/m3dWqL3hUKrzwAvX7ex5srapj8XbyzpCDrpZxrbxzXH+aa2YxfqZ 9K4cjkvhczGvLo2pxUoml4bUxR/lO2GwkyhkmplDBrSsEwv4Htj3KShrkllK Gp8MFO/i78cFildWb5nVpIonFnvyQ1DSlh/xF7OV9N10UczjR2P53WRF8NoB cq2fXb7b5XQMJHtyJo6PkIk3V9I1q65g6Kj1iLR8jPz2VOMlI9oN1GEnWL3c NEk2PjR7YTBVgOnL2jmSH6fImx9rOMUFJShUeCO94x8Sal0b7SW3MOJJgjDM Sk3ynA64M9LK8X647m7j7Z/JpLj3yc2m91ESdWx8/V4atHKIzBjDhxifP+f1 94QGhJ5K2Rw1KUVa3xDUnKZDQ56jkqivxNUnAiK9OVpwSucAi1ddha9VV/cs fqwNaaYVWlUXHqH76NHozIiFoBERk16YVoOerzNsGAwdWCPJXLolvhbHG4Wx LWWLwfvRhNF5Th2u1ZebuxxcAu7N29XVVvWoQ6r8lFNL4X0xlC0yaMBtbwXT Fj7LoMHqwwYTg0Z83nBIQ2CrD6GG39nF6DVhxbmmAyyVPrTK7ekL1E0YoCUa ksmWg6/jYLHnzBP0Px5VoZu7AjLDmCZVo09xXaCNjOdnAEX62gsjZc3Ytdx2 scjha3i3p6Rluq0F/yiPv2ZLNwRlyBA/p7IVozQ4OzsGDUFzTX+NuqINdZSn 3UKlRkD/Pvjag3vtOFrCzso/Ywx3tt1wP5/bgVlrTDSrfUwgcyS5fVV2J2bk BjT7sUzB3EvPfDhBhoKs/TLdN6YQZ+Mw/jG4C2dci2fza83gone6q9C+G0dG t0Y2JK0EuznenKK0GwucNph1+plDuOjP6xute7AsUaQfyGVALNW9inWzB5N8 /HfQVQygh6dOVBj04kalpDSpkwmmAxbXbS71Yrb1tbLOHSzQ4y6wt1vUhzF1 adk7qlmQ6dUiNU7uQw8zn+I2Szak3Nn30y3tfvwmtHmffjIbfCY3m3ZG9WP+ SqFlh4oNj7VmS7vU/WjZ+OsVz30WME2nW/hHPMMMbgOnt9YCija9pCSjzzBg SrPny0sw4px9ss5fjsL7H1nJFwhQc298Dnshx+D43XPuFwngji+LilbIUbRb SuleIsC3RDyTMijHcypResYVAu4yjkwVD8ux3GH209U8Ao7p2Y8pxuQ4Wz8v L7lNwPPJ1v5tajlm9OqmNTUTcOeh6jbTjMLcwpCgX1oJUIYFWXPNKSw8IXNx aydgka2ixJFJYaVhhrpdRoCwqE7iQ1CoFKwI6ntGgNHl1KupNhRajZi4vBoh IOEkWzy9mcL10tOMolECpHZZNC1nCh0TFbOH3xAw9E777HKgkGeVd29snIAt gRORXFcKjx9jMT58IODd3t9D/XkUntkSN/tgigALA85EuCeFiUte9Z9QEcDr vn7k7E4Ks+8Wps7MEPCbW/yhHG8KC2I1Ax+pCejTVA2X7KHwttfhrWfmCNCq Dzwo9aVQavHU3PlfAuyiB5T1Agprp1bPzs8TsN/BQ9D1A4X/AbMLY+0= "]], LineBox[CompressedData[" 1:eJwVkHk4lAkcgOWoZaYVLSXm/KxbtE+1peP7dYscGbOiXWuGQdGIh7aQlZJR qVGzcqzHuropNxU/H0pDtEVSbDU0FalomuRobfvH+7x/vy9HGOEl0tTQ0HD7 yv/OTRDOXhJ0fC1df9SR3WfZ0NLF3ubD3kUym7cOMAZ0cOZ2w2E2+wBJCnTt 3imMMLcxjaXDTiU9HIc8exTfY/iamD3jrCyyd4FvYJtiGXZNhcpGWRfJTFp6 eItiE87pG7B8y6ojE3TsIykFH/Pb8iLfsOTkXs04FSpEWHo1tS988ROSWbPW y6djH4aQ97NGogbJ7i3Lp11GE1GstB6sLB0iNZ+yxab+R1GPc8Ty2YpR0vXe 43c1607gyXntNvkBKvK9ZCnt5+dSFPZ5o9bdT+Qdn0CLpidnMPLWEWGE5SSZ PjX1N7RmYNleOm/h1i+k/p0Z98hDWZgfFzbs6KMB+k27u1P2/YlJedPbP47M gtoXYO+5Mg81up7DzVgtcBA3Hls4/hdaRAfv97bRgWYNmea0uABfqM/+RKuf DSWWjKDajkJ0Ue4+eDryGwhQ+spfbS1G9xdSWyZTDyRprvsIPIfDzcLEOyU0 oLV9oK8wvYCLDXoYG36dC7xct/Mou4h6pFrQr/oWXmr727LVl3DLW79xLn8e eGhxK1RRV7C3KWiWn50BcEeyk7qGSrBK0uLPVhsAb5d81YktVzFYJ+Z5Z6ch FDXwp3cKrmFgVFwVPXs+tJ/O9/A3LEOHENvObYLvwLG/9fZLLMN7hna0mJVG MDbailbx5XijNCnHTssYnt0rsH9kW4Fxs2w87/5jDItjfRjkcAXq9cc6iysX wK2sl472xZWoPMeR5cUvhIOHPetSeFUoszLRruObQOYKWXPOvGqUZge3CtiL 4GlN+Xozqhr9ZL900l8tAtGVy0quuAY/byyeyGswBY/wBL1B61ocVK7f35Ri Bv6fbIv0H9diwZolph0CBvS4VqA6ow5LkmMMQuyZEBNm5OnsfB1T+IGuWmom uGl4aXM+Xcdl/fkXUzpYcCog1Kmi/AZmWueUdLiy4csxX2WZ8Cb+3piW6VrH hrZEc8PdnHp0M+UXt5lzoPuNXHihvx7XiVt3GqRyQI/jYsU73oB5ZkLzu2oO 5HGKImqcEc2bz2e47+RC4EivrWQCUWrfZPOggQsOxh+TI3iNGKzSvi+3IUCR 87r6t7JGFJZ9YKeeIqDoqAt3uS6F4Um8aZd0ApaPJ7yt16Mwhlf5iH6GgNaQ itpNdAol6piT0gwChpzNPPj6FJaunJg6m0uANe1dXLQRhRPUTM+5ywSUnkp/ WM6hUPqAntbSSkB1Zq/EwYnC7MI9oUflBGzWnetds4rCwujODc7tBDw5sI5F rqGw2lg62d5JwKTfpSp3oLDfb35o10MCVjHiB/ZsptBy0GTDwCABVD5r9RUv Ch0rY5lFSgK8DL3nLPWm0Cm5b0L06mtfkuTBDT6F2yxzrw0NE6AZNBbavoPC qDA2c2yMgI0WzX8M+1MYv/rQRLmKgJ6M8YCoAAqT5w50R6sJEM2xs5sUUJh5 tfD4588EJL+WNemKKCxI1A65PkmAia88LT2YwsvbRevjpwk4L/+ywySUwkru bcbafwn40ekH8/xdFDaoLCZmZr7+uxT83iqMwv8ABlFjyA== "]], LineBox[CompressedData[" 1:eJwVxXk01AkcAHBytCsUIkfm8PNMJKl0EP2+yXsJ9Wo19KgtYxwhYs1TKNc6 JkvjKOfs/CaV2pZSareW+YZyxeTKEb3kyNIhy8QgdvePz/swOWE/+K1QUFA4 +J//F17kqG7hpu/5DK3bf9+tKnnWyXDzZJwmOe2Vvyn7jUiW6yVJDMZ5stHv +LZe7oxE+DSDrsLgkwub783WcJUxxIF3ZpZeQK7Vfd33iLsWOxcCc7/Qb5PX Vk66VHBNcWX/EOsT/TE5Fn8+qZxrg+JmUfgHehOZXi2hl3GdsPwuvz/E6jXp eHjzLQdgYwDZXvAxYphka6t5FmefxNBR8+HK8nHSRClpPLuXi2rMn1lvd30h 3WZLnSh2EGaueWEhPjVNort28HhkGHL6j6JSy1fS5tWRvG/xERj+/GdOGGue XGrhWGbZ8bDirLq7/oFv5OQ5vVLH51EojgmesPZUgHnxibO9KdGYKFo8MvNR Eczj9tN/MbiACp2DUBWtBNJb5xNcRHFoFul/7qiFCjSW0gu+bkrAEVmex6pq VbB95T7SHZmILqNBF7LDv4NdNe0e5j1JeGhEsJFGU4OIzmkTxW3JOFHHiW8s WwVPybF3AVEpaKXVbbzvpAYUBJk2Qk8qqpEyn4FpTUiZ3Cq+Refj/k9esybs NbC0NV2cmHQJe2u5il6WWvCgOHXh3WA6Pkx79iNDpgXRp9jObWYZ6K/CG5RK taFlKKTKOi0TfSNiHqoX6oANsglGx2XcHLBR6uazFiZOTYU3XxLgS23LVTxb XUisGRh1sMvCv8oTiyyV9IB4ad059yYLYxQtDre80QO1KvOukMvZqDYQ7Rxa uQ5WV80klDjk4OhNZq4oVh+MT2+4zRzMwdwNBsqP2QYQLlMYOSbIRUGhf4MP wxBeWjnm99hcQa/cE1L1MUNwjWHL9buv4JzTDblIYgQapRqhOslXcXjU8Vxt 6nroi7M6zt6Qh9ccthi1+hjDh50zJw735WFZMk8rYBMNVIUmfdkX8zGV7euq JKMBqUso5jMKcPuA+HZqKx2qQxrtPdoKMN+8qKzVlQHO4d1T3pGFGPc0I9/1 MQP02fwnhmZFeNCIfaPZlAmqbprWxV1FuDe0wVuLz4S5yQWaX1QxitZzTFtk TLD5KZM5xhKiaV3p1UPeJhBbwhfeaxGiYFOtRYfEBN6+96i3D/0V/aeV25ss CEj/vmlForEIORX/MPiXCbDvK/lTs0aEIYnuiy5ZBORVdyiM14mQ517Zo55D wKRY8UBdvQjTZLxMwVUCSoJO9kW1iLDcVr6QJyRAbdFwfrBHhPKa5e6bdwjo omXvfvBZhIIO9YxnDQTs2ApvN2pSWFhyJjCliQDf655KBaspLImU7nN+QYBA L4ylqkXhIz3B/AspARPzwrBBHQoHvHQCO18RUFy3sJxrQCFr2GDf0DABK9h/ MJZMKbSujKZdHyXAqkHqFGxGoV1yv9xvjABv2/eBvSwK3VjCe+MTBFQa61bc t6AwIphBm5oiIPB9xN4Aawpj7RPk96cJuHLskl/XFgqTNYa6ImUE1DaL+Xu3 UZh/tyR9bo4Ao7tt7UY7KLwWrxzwZJ4AZ+bfsrSdFN454ucYu0gAL2fZ4Osu CitN6o33LBFAqazb42tHoWTaTL68TIA0yorTtpvCfwFZPF4G "]], LineBox[CompressedData[" 1:eJwB4QQe+yFib1JlAgAAAE0AAAACAAAAnX5iBjFkiz6BNOK12I7IOsTTIExX IGk/46NHiSIBo7v/xr6DICB5P8KCw7XLaoI7ncCNHwUgiT8UC48S67a4u2w9 dW33H5k/e4BHycNf0LvT+2iU8B+pP8/3HSUZCMi7B9viJ+0fuT+wfEfJCwP9 u6HKn3HrH8k/ceA7SgSd2ruur4nbbC7aP/rw2GqSRru7Zz/Rmexy4z/4tF1O hSwZvG7lKeO0ruk/BR8P2odBBDwKIYQn3zjwP/06Aro7YzM8jhDLKqFg8z8O Y6AcHVMTvGLbVL8DzPY/9DIp7+Z1LTxxxYRibyf6P7qdUZNStC68sXAMUxhJ /T/3jpd61XZJPKF7a+owVwBAXAj3WZ1WTDyCn/xR9OwBQM112tNUY/O7ANPg QLx6A0ADvTGnKn9CvCZ0ZnhUKgVAULld8OiQPTzk9ZdWC70GQMhBNG9MvTc8 SuVqfZJxCEA+0PFtb4EyPE7kkCseHgpA4btKk0TfM7zqw2KAyK0LQEmD43o5 51E8LhHWHUNfDUAT7ia1g7hFPAo/9WHc8w5AJYCRNN2QQTxH7Vr3IlUQQJTV IBh3lTW82MJkAVosEUAFxl6ZwbE4vLWIxF4g9RFAqrBDzX34S7xmBXXgzs4S QEztkTe+MCq8Y3J7tQyaE0CVZIXxfm5JPC9nK85MYRRAmht52GuLVTzPEiwL dTkVQNGMUnAOq0I8u66CmywDFkD9Z+x9j2wSPHsBKlDM3RZAWyA43kW4MjwK 3HpIbrQXQBGGfW452E085aYhlJ98GEArNE1vjxYdPJQoGQS5VRlA+UlJ7U/Z SzyQmmbHYSAaQAE0ponuEFG8WpRdzgznGkC52CBsrFBHPPhEpfmfvhtAcpyB a/euSDzj5UJ4woccQIbqJSpKSDe8oj0xG81hHUAC/5K6Hc1mPK2FdRFnLR5A d6ApWdiQKryHVWNLA/UeQGnORCSdEf47NdyhqYfNH0D+475LbcdTvJgpm63N SyBACT37eQ9gYTx/wI2YS7kgQKKZpXOjHVI8TRtVpcokIUA2yljNVscyPEFu x1sRiSFAfr7nmSPlQ7yfHGIkzPUhQOmgd+W8fUg8JMOnlk5bIkDgquHkEm9H PJAtwirSviJAOazYTeU4W7xm8wTRySojQMbYUBwt5028YrHyIImPI0DuojTG POQ9PGyCU/xKkSNAjiN0jpA4V7x1U7TXDJMjQOy3OicMlWC8iPV1jpCWI0Cy IeA50TUwvK45+fuXnSNAKXP6HPUnT7z5wf/WpqsjQJFvHjr8gzW8kNIMjcTH I0CEYJwOEftYvJqjbWiGySNAZ9ZOp2a2ZbyjdM5DSMsjQHSDsJjEUGM8thaQ +svOI0CskaEOtEFYvNxaE2jT1SNAamFThxMkabwn4xlD4uMjQJKSWCemqma8 MLR6HqTlI0Ac6dgUG5EXPDqF2/ll5yNAcHtnnR3xRLxMJ52w6eojQNrUpFgR 0mo8cmsgHvHxI0CMeETxmN1WPHw8gfmy8yNAvtO8zvxTU7yFDeLUdPUjQP53 UByP3nU8mK+ji/j4I0AnLrADMgpwvKKABGe6+iNA5gTCzo7aUbyrUWVCfPwj QJioYQcbRmG8tCLGHT7+I0BfJ7Fzbp9zvL7zJvn//yNAzzsWOrGJ0DvHZz9b "]], LineBox[CompressedData[" 1:eJwVj2tUjAkYgGd0YSutSlFp5pu+TqMkiUg07yudg4rDZsoJS2O6qJRSJwrd pEbKdNF9zDdCrK1kh10kEt0b3S/KShfttG5tja521v54zvPvOedh8UJ+8llA o9F2fed/i87x1NfyUzhfsNnu183qnBfthJsncQx4rdJfVH2GOcqaygSCOA0N PgfX9fAnOaJnqUw1QgBza+5OVfFVIcgx4vgUMw/09F/3PuAvhfY5/6wvzNtA LfzsUs43g4V9g+yPzIcgjz2dUMpfD5IGcejfzHpIe1LJLOE7Q2mZoC/I+jXA njW3HJELftCa9yFsCPbpangWZhyG4BGLIWmpHFaoJMgzevigwTrPfmv/BXZN FTtT3ABIW9JoKTkyAQ/cdQPl4SHA69v3VKXpK2zo3JvzLTYMQl+e54WwZ2G+ iWeV7hAB5Se03Jfv/AafThkUO72MBEl04JiNJw3nJIdO9FyIgnjx/N7JD3Qk Y7YzLxmeBVr7AFZEqWDnrdNxLuIYMA/3PbXPUg3ripl5X1fHwbAix0PziTra d7oPd4XHg8tIwNmM0EVoV9XqYdGdALuHhasYDA0MaZ8wpa9LhLFqXmxdiSY+ htF3fpEXwFqny2Tb4cVYEGBWh91JoAEK7/4JbTz32VZyiymA7R+9pky5S1Bp myKJT7gIPc/5dC8rHSwrTJp7N5AC95Nf/EwodPDkEe6OFvNU8FWLGJDJdLFt MKjCJjkNjoZF39fK10Pbp1ySaLsMa/xWydy8l+KHI+OhDReF8ErXSjNikz6e r+ofcXRIh8el8QVWKgZIvrJpn36TDtF0yz1NbwxwUYVFR9DlDNDoj9oRLF2G 2hWTcUWOmTByk5UlPrMcmcdW3mYNZELWSkPVh1xDDFfQhvcLs0CY71vrTRhh o7VTbvf6K+CVdUimNWqEu6O5M8u7rsC0840ZcaUxahQvDtZLzIahEadTz5NW YE+M9UHuyhy45rjWuNnbBMc2Th7a05sDJYkROn6rGagmMu3NOJcLSdyjrioK BnL0SXoukQd2/ZLbSc1MfBxUt8WjJQ9yLQpKml0JdA3tGj8Qng8xz1JzXR8S SHAFj4zMC2CXMfdGgxkLF7hp2xR2FMDW4NoDOgIWTn+eY/hEFoJ4Bc+sScFC u5NprFG2CMyqi7N3HzDFmCKB6G6TCISrn1u2VZriwHuPmi3BV8F3QrW13pLE Sz/UL4g3EQOv/B9CcJlE+96iP7SrxBAU7z7vkk5i9pM2mrxaDBHu0m6tTBKn JPSd1TViSFZEpAmzSZQEHO6NbBJD6aaZuRwRiZrzRrMD3WKYqVJ23bxD4p+M jM2/fRKDsE0r9UXt974tvl2lTUF+0XH/C/Ukel/3VMn7kYKicNm2HY0kphuE sNV1KHhgIJxtlJEonxWFDOhR0O+l59/eSWJB9Zwyy5AC9pDhtsEhEunc34l/ zSiwkUYxro+QaFUrcw40p8AhsW/GZ5TEg5ve+/ewKXBji+7Kx0iUmuiX37Ok ICyQYIyPk+j7Pmyrnw0FZ7bEzdyb+P67/6JPx1oKEhcPdoQrSKxqkAi2rqMg t6woZXqaROOyllbjDRRci1X1ezRLogvrL0XyRgru7PVxOjNP4slMpeFXewqk pjUmnH9JvKq2jHPUgYLKCfMZpZLExkhrXstmCv4DXdg3bg== "]], LineBox[CompressedData[" 1:eJwVkH041AccwAkZzopGiXO/u5854Yo91ROV7zetdVHCuYmacV6LznhohTUp oVLUTV7y6EgvRJ13FeeH4YhWIsW2jq4iNXVdOjRrf3yez9+fD1MQ7R26QEND Y8dn/nfhYcFCx5CTLoaLphyIYbZLez+x3ZfYCxZt20bpozow39F8lCAOgWuQ nv0buQkUtmQydIgM8HAY9xyUfw1RG+P3TzPyYGCpX3C3fA30z0aIphjX4IJB dlS7fAvoDo+yXzMaIUGHE0PJ+SDuLop5xZCBcEGiUioPhcobGcNRK58Avd7F 27f3AITD/bzJ2DEY3Lp2zm0qGYSKFWM1leOg+RchNA84DvrMY+y/100B3nv8 pn7TKTi9uMdWHKgEZfpqgz1Ps0Aw7CPVuvsBun2DrVufnIOY348JotkzcGF2 9g/szAHJTzTesm2f4MuueY+YI3kgToyccPDVQOPWfQ/TDlyAlKI5r/eTmtjw DDmeTkWg0f8U7yRo4Uphy4ll0xfBOi7soI+tDnZqiBbMCYvhmer89wZNC1HC poc09JaAm2LfL2djvkB/hZ/sxbZS8HiWZWdpqY+nMt0PkNLLMNEmSO6qMECD 7ne0deZXYaXRIH3zj4a4s3DHFanoGuiDKmhE+SU+1w6wI1RlsPW1/zSLvxjd tVjVytjrMNQaoulvb4Q2k/kp/eMVUJveHkCojJC3V7b+1NYbEKYT/7Svzxgv NvPndgfdhODYxFpa/hLsOiveGWAsgVXhdn3bg75Czkhnx3OpBO4Z2xvEO5mg aqpTapNUBbcrUwrstUxRfq+Y88iuGhI1bT3v/mmKjgm+dJioBv2RBK6wZil2 5T134JTWgOIyU1SUtAxTjno2pvFqQWRjpt3IN8OCdaK2gsV1kJUf1hlELMfR +ipXC6oO/EU/9NFeLMeQ6+UKlrAePn5bqi5qNkfPqMP6YysaYEzherA1zQID P9hdWvS4AYo3Opr3BtFxyL1aqspphIrUeKNwjiXGRpp4crm3II0f7K6lskQv DW9t5odbsGZEfC2tl4FnAyOcq6tuQ+6KgopedwJnTvgpJII78GtLZq57I4Fd yVbG+5hNsMOcX9ptxcSBVzLB1ZEm2CTs3G2UwURdppsN72QzFFkIrO6qmChm Xoqu50rBqu1KjsduFu6ZHLJLV0shi9Nq+6CZhY6m71OjeS0QptS+L7MlUV7w su5nSQsIJO+IjDMklh13Y63VoyAqhTfnlk2i0/Th1036FMTzah7RzpHYFV7d sIVGQboq/nRWDonjXIud/EUUVDqpZ88Xksg2eJMYZ0KBmpofvFxOYvmZ7IEq JgVZD2iZ7Z0kVuUOpa9ypiC/ZH/EcRmJXD1Dn/r1FJTE9W3m9pD46NAmBmyk oM40a6anj8Q5/7JaD6RgxH9JRP8AiS70pNH931HAHjPbPDpGYouYseG6NwUO NQmWlxQkehn76K72ocA5dVgd+uJzX0r6g9t8CrazC2+OT5CoFfI2omcXBbGR hOXbtyRusW77bSKAgqQNR9RVShIf5kwHxgZSkGo4+jBORWKorr39TBAFuTdK Tn78SGL6S1GrXigFxcna4bdmSDT1k2Vmh1FQ7hXqmjRH4hXZp11mERTUsDro Lv9+/uf8jZV4LwXNSmv1/DyJHWVh/9hEUvAfp0U9Xw== "]], LineBox[CompressedData[" 1:eJwVxX041AccAHDtUEmhTF7vxU/JORWPnieK73flWdKxFOqupTlylNfmypLU ndIlklQoXUdujxq9OEaZeSvv57X7TccKWSMtZTfuUrb98Xk+DF7sroNf6Ojo +P7n/wtO8vSdw9I9lQNe2xnz4NnUR2fvoUfC7952p9o4NjD/tFZEp/8AgZXD p89znKCgLoOmRxeDcXSd8BDHA6I8BNEztDyIbFkn4nJ8oe9jRM4UrQTMj/JF uzj7YaFqxP4trRrUbJHIjxMN0jZJ/BtaK+zdeEnE5iRD2T2xKmrtc2CFuEi8 r2QCH3ryJo+MgvCWNUW36irEjDmMysvGYcuxxssrdW6CASPV/sXGKWgstxow nS6ETON2pvS7aZB8qGEWF8qApwr4ldLxD0CtV6Or9A7EP0nlxdprwdcj2Iea UQYP4gx3m2//BOdOvxM3Wz4AadLhifV7dLCTSWSnmJWDUDLn//fkAow7dn5T 0pQcdPpeYs1xCjYUuA8S9ZWwOiE8MYCphwkGwXR2dRW8Ul8LWvKLPqZZVuhV XXwEPmOHkrPjF+HnuJTMoowa8HuV5UilGiBLmr1ss7AWJhp5p1pKl2DQo8mV F5h1sNZEabP1wFL0ad6urbavBwNQhwxOL8M3xVi62LQBtr3lztgGGuMT+/fO FqaN8FtD2AIuywTjzb52STFqgopzTcF0tQm2KF0pC7VNEK4neKlQLEeu+1Cx 3+wTCD2SVGGYvwIvxdIsqsaewjq+o4IdYooyE/1FiYpm6FrOWiJw+xL/CJK1 zLS1wOMy4XUWxQyHol9y8ipbIWkBc2fHkBlS1vTXaCvawGDwuHeMfCXqfxN1 /eH9dhiTMXIkJ8yxbNtNnwv5HZCzxkK3OtACc0bF7atyOyErP7w5hG6J1v5G NsOpCuDm7FcYvrbEVEe3iQ9RXTDrVayR1FphVkCmF8+1G0bHtiQ2pFmj8xx7 TlXSDYUezladITYYJ/jzxgaHHig9IzDhO1FRRHavot/qgbTA0B0UNRUpcemT Faa9sGFQWpLWSUPL57Y3HC/3Qq7D9dLOHXQ0clro6rK4D1LqMnJ3VNMx279F bi7uA1+rwOI2Owam/7Tv+zv6/fBVTPM+EzEDg6Y2WXYm9YPEmmfXoWbgYz1N SZe2H+waf7zqt88WP1EotqHxzyDLqYHZW2uL0o0vSOnYMwif1u1pZRI44pl7 tC5UCbwHH+jiiwRqnW5+ih1QQpRw95zPJQJZE8ZJySolCHbLScPLBHJlotnz Q0o4pxZkZl0lsJwaOV08rIQyN83HawUERhi5jqvGlaCpn1fK7hI4MNXav02r hKxew4ymZgLvlKvv0qxIyC+KjjjbSuBgbISDkw0JRQmKrd7tBBqwVDJ3GgmV ZlnadgWBYbfrpIEECYPcFRF9zwg0v5J+Ld2RBPtRi60jowSmHmWIZjaRsF5+ nHp7jMCHLjk6ep4kuJ9RaQ6+JvDFX/onlyMJbPuC++MTBHryJxOdvEg4cphO ff+ewHd7fo4JZZNwYvNpzcNpAm1NmZNxfiScWTrSn6Am0Lf7RuTJnSTk3itK n50lsMRbGJYXQELhKV3+Iy2BpK56WBZEwl3/g1tOzBFIqecfkO8lQW771Mbz M4Euyc8H67kk1E6v1szPExjs5svt+paEfwGOpD55 "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotRange->{{0, 10}, {-0.3650396711208453, 0.36503967112084534`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{3.4703117682274046`*^9, 3.470315063915637*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Energy", "[", RowBox[{"1", ",", "U"}], "]"}], ",", RowBox[{"{", RowBox[{"U", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470311789402405*^9, 3.470311805185405*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwVxX041AcAB3A5anHKRfIS7vzMyWtn1dLG7+v01Mm55eVcHb/MFWp5r1sl a3VL8hi7St6ax4OVx1OUoh5L3hfCrSNUriYvT3kb4YQy2/74PB+WJMYvTFND Q8PnP/+fd0ayknMo1T0zaoLjdaewtqmLyRcxj5AhwiA/9tU4cvlxzU9M5ily Lmx1U3TxDTKvLs1Sm5lCjhnm+Cjja8lIN2nUB8scMiZ1fe/sAyXZ9fFwxpRl CRkmvzWScHaAXNU3wJ6wrCIJj2Pjx+qmyYIn+XFjlq2kqE/R916pibLbKX2R Ti/JJd3coyEFBogglTnj8YNktIco8Yi9OaKHNw1WlI2QBX5slxIuAR3WefZf 26dIj3bBFE1oi3T9NruCb2fIOdld1j19R0j6Ampp7XOkobOtyztjDuL+OC+J YS+SQ4x3gYl5X6A8lu5v7LVEKqTuFx7NbUXB6aOjm0UaKK/6VXFfth2y/E++ s+MrELrGOZ0a3AGNrn5UJ9BQrzRV6Gx3g83x8JMBdtpo1Jw7EFtLYkidFaj7 aCVKWvS66/U8sGf4ux8ux32GE+mCEraQC8GQ3N7CQgdUeI1SnumJ0UbJ2ZZS XRCE6/Dehp1wYvSYe4bo4UU0xyFq1S7okOpQ1cwa2Di0Sfq37cbuCfEHK6E+ ILdS3P6Rh+cNh1aIHRhYMDuUJWvwQuXFpgNMNQPW7t0Btyb3IFxb2q9QrMO2 p+C5bOPjYPzpSnquAdxp1zhrI3zgHGGv4IcawvThicTJSwL8uc5BV+q6HmN6 /Uv2Pd/gYZnsmgPNCG875A9DZHtxeoXd3vZXRvj5q+QrIhtf6KgSeNEVG3CJ 27LRt9kXwzdYGfmJxjBR5lh9T/khw9ZEq0pogjH9F55eGv6Q54Y3hzJNYVU9 +WZ3tj/EGZSC/tYUrC1vODzHAMzvvL6QX2OGLAPvvDlFAAaHuScbkjfCTTCU 9DRMiEI3jllHqDliImZT9q0ORGmSlBHhaAE6jdKlFwYiWXjQm6a2QKVqxL3+ SxG2qgpKkjssYTQ9mWb9UoTsTddKO7yZYJidF9+L24cf69KyvauYqOanc6fW 74ePmfD6E2sWcqO6VU4P9sMjujmIkcKCltOz2WwfMfI3Sqzb1SzQN/Fsy6fE sG4szhQEWYEuSH4xezEIcscGu84aK3C77dx2WAQjfEZL2WpHoKjWo9qxLhiS 8mlmyi8EDLvdq/giCpEy/097LhFw3hcum9xPQepf0Uu/QmBXb5r35WAKF9XS dHkmgROtqle9oRTKXBc+ZuUR0DyToHkwksJC/XLPjZsESm0rvU+doyDvpKc1 NRPoTGW/vn6TQm5R1OELrQT+lguKeWUUio4rPHltBD6/LI0du0PhvpF8sU1B QDulUZNzn4JKbHC4q5tAIi+EXV1HgT1o4jkwSIC7NjO2s5vC5ooEi9+GCYz3 VLtKn1PYkdS3EPaWQEvuoKZxHwU+O+/OyCiBDRs4V6l+CvFHmRbv3xNwGWir ejdKIfHrcwt3ZwikpE7LUicoJOkNPDuuJsDgmPCdpihk3y5KnZ8noIoNf31M TaHwrFbE74sEzHXTio3mKdz0DeMmfiKQU3AvtmqRQoXVY3P3fwj4b3npGrxE oWbGZmF5mYBfowZteZnCv2TGJ3s= "]], LineBox[CompressedData[" 1:eJwV0Hk41HkAx3F3m2OLyrpnxk+so6JD2VW/T5QUWdegUfiOYyiEnelAm5Qr qSnTULKujqfaRFFPbdQm5EhbVrtFsph1rDaZGTnXtn+8n9f/bxZ3r3e4koKC wvbP/W/hD1w1u7DsDYOzD8VPu7IfPmlnuvszo+gP9FqlRQml9FxD7VEm8yDt H9fYav5XFV34KIehysyin6902KVYWU9HrxfEfGKco4ecm+xbBzvo9ulI0Sjj Kq1uWOnD/CSh53X2Wrxn3KMlNV1H70/J6ZLmovi/GU103SzvQfG0KspvZnVG L39Dt/enVJ8Y1AWPfnFuJKGPLp5a2pSpwkKsxLKvqnyIFrE0cl4fMIc665jF u3WjtE7ricbUUBucXNhiVRIipe+SAn62zBbcTt+Hyq3jdMTd22NHxlYhvv4Y d6/FFG0a5bA9pdcelXGaPnpbZ2lZXjwtK3JASdKeYVt/Bfglnv5JlO+I1KIZ L9mIIio2t9+5FkRDob0HDxKV0U+WsMM0NsKcH3HA10oVwfMLcuanOaFfnuen UaMGg7XB4iiJM7ZJdh86E/8FXDrdu4NDN8OjX2htYqIOeW69IeeNC4bruClP b2hAt2651YJ1rliu/crYOVgLfkpz+zm3t0KdlpMu6ZeIFEyJQ5a4Yct7zidT 9kLoTEfLZ0Tu+ONxmCLHRht+VgNbC7U8UJ35JIgp1wanu2HvRPR3iFAV9LS1 6YDUiodlfE+EJiRVa55fBDI7T63F3AsreNZt7mQxHBaLjKgOLzzXsdEQOCxB +sYBb5cz3vi5PLXARlkXdaUqYw1OPkhStPJsfauLnZKhCh0lX6h3JbrGVn0F 6dvR3T01vpBcZomKkvVQ69icoxHDhuhrfZV7bH1cq4j+VdHaD8LzEY2EaYAN upIkdpcfOKJdbZoDBqjgpZtaH/fHxKZLk0W1htjj/3GwxSUAfRKnA48zjBD3 o71e83gAStfbGT4jxtCP28zLrd6BG2kCbd4yE3RcsWXc53GQwQ51U5ab4Mx+ 15dc3UCs6Sq5mvGMgZWjlpdetQci37LgxjM3JgqSh3uuHNuJw49y8t3uMTGW yXfctGkXthuyLzWbsRAQZZPLVQjCxtjGQO0sFnbE13t33wxCkRHXrFXOwtQ/ FiuXxgbDrO6K2CPQFMu22Nf0LwiBcNljq5e1pgg+NNr9KSIEEVKVF01WFM5x Twnj6kPArRxjZp2ikK5aPJ5nTBCd6jOz7TQFbbezYhaDQOBT9btmLoWjwuP2 15kEmXLBSaGYgpGhYF8tRVDuMDmdV0jBYMW28X5Lgslf5l5dvk7Bx1smt7Mn EL7UzHnSSGE4zVXe4kFwviwmMr2JgufT9WfZngRl/DZn1xYKF9RXrXnnRXBH VzjV0kZh5KSxYMyXoIuzKLK9g0KYeEymF0hg0afv3NtH4U7xBVk4j8C2KtHk ooRC7p+nRR8iCb5J65wMH6AQYJqx+uBuAneLwoqhYQrisnj+iRiChD1Mk48f KUgvushufU+Q7Hhk8paUgqbkW5GjgCBNq/c3vpyC1lK71Q37CPJvlmVPTFBo uWjIf32QoDRFhXd/6vOP/oWLQ5MIrnuFOyXPUDA3U6saSSaoMm0w3vAvhYrQ aZ99PxDUSs0n5+YoMMtGpXOHCf4DSR0xOw== "]], LineBox[CompressedData[" 1:eJwVj2s0lAkAhsklZ9xCCcUMnyVCqd3Kbvre6KJIhHHb8A0GGSPCIZcktlQT SZFoSDjWuhWdLUVLuTRmOmVTG3u0M822lBKNZmSz9sd7nh/Pj+e85qz4A5FL lJSUPBf3PyuyWOqOEWe2hf3FS3n2PqbrwRDDw58RQ6rXfmOsta6RXOjtPMFg pJFia1LiUN5B6hTdaqG9yCFHV54/coPdQ1bc59HVGPnkvMYvH7q6+0mOc3Lc Z/pl0oMjvqeh8Zwc+hJdPEWvJyXZci7P829y6YjYepJ+mxTQDJo368+SVY/4 CW/pA+SFPG4MX1kdTc35IxyHl2Sa6tjk13FDRJFPLr9LlJAnSrZmqamZgyu1 kbQ1jZOW1ZvVtqRZgWaeaz22ZYrckZBVJAy3w7llAtuqsBlScPdFz8+f1oM1 4tulMjhL1hG0wvLpjUh4mMuKt54jW374NrtEvAmth7V8jPb8S15QpH/WqHRC VXrsxHp/JehVXnSuK92KHP6896d3ymCJr1Z3hJBQGnqFu0dV0JrRYsbR3A6r JHaqr60aIh5xfl2W54LXshKm5j11WDNdXQ5LXbFXeiizKEED/rE6BuzwnfB8 XbjWzIwGofDmROjLXZjoYWX3N2qCX0/WLN/iBge9YVPXUG2UGzlcC725BzRS Ro3O6OCdY11m5Ap37J4M+mzhtwzGAwfKlC964EV3hHKQnR567cvaqrQ90X7q QQhDpgfNGKP6ec5+sNWSX4lE+kgzEr2fTfJCeGJ6u1aZASZ0/WWDVt5YF7VW 5EEtx9VuudzymTce69tpJjutQMTugNVuRQfQ0ZRzxU7FED3DKxr6XXyQrmzr NfinIaQ2OYHLl/iCNnrUjdu2Ese6clXF93whrTUv5mcYYa5uj4l2nB+K1xir 3vYzBiezdr/KWiYKy9h9FMMEAftyPjBHmQgqPijSemOCjazYM3an/SHfUaPg d67Cl03iXcJdAZBIXVK7T66GYUYuRzAbgGvOjquElCnYs+2txe2BaMxL1ouy N0NF/9uwjqggnPQLd1eRmeGSybhmhGEwvhutqj8ppGOMdWT4+VAwSm2uNArd GThPf0yrz/0Rx+7zSt1vM1A5eidk546D2LfKr+aRpTmirzObwpVCsJ3bF6yX b4646PKoseYQ8FezLAdl5iidSoQVNxSWPXWXPIMtwEo8vF2qG4ZC+27bp50W ELRxwuTsMLBnVJ8M2BJwctqgm/AwDKzWaUZ+AYFx/q3EUlMKnByf+b3nCTTf r9S3oFNI9ml7rnWBQKjk9I0GBoVTsuRzhZcIcB1CpzsJCk1Oii8lFQRcR5Ym Sm0oKH5bGK5tIBBSEJiwYROFwqdavAd9BJ4e/Bo/6EmhrDou+qcBAkl3/tFl elGoThK5ugkW+0ZDzWPeFG4ZFs4JRAQCR+o+TPtSGA0yiB56RsAxxTveOJiC tcTYVSxZ9Co1XHYUhfVtR82uSwmsySzQmYqm8H3eiCLyDYE+eVpT2iEKHtYV LeMTBGJlnu/PxlFIjGWYffxIgKmqiLt5hELG1uOKGzMEeGcl2s7JFPK0xb8n yQgUGIoae1MolDZXn5HLCcyuq578I43CtWzVqDtzBPy7eLzwdAoN3pEuGfME jnul2k9mUGiz6DXd9nXxn4QlTMmi0DljpVhYIOCQui9OKZvCfw/bMfI= "]], LineBox[CompressedData[" 1:eJwVzH081AcAx3HmocZZHpZJxZ2fItSkh6nJ7zt6jUWWZ04nd55+Og/RWUiS SBJuRYld8tiaIdvllYyVLCtcnEZFj8eKkOg65+nW/vi83v99GJwYj9BPlJSU dn/sfwUpHPWNIdn2wnL/qE7xQ/u2XrqrLz2CTHcez+1l1ZOKOy3H6fRE0rKv trnB9iYpuJljrEbPIgfcKxbH6u6TkTvio2TGF8glT8WhAUnPyN45Kn/S+ApJ M5ri5kS+JZcMvDQbN24kx2NGdHUiFGTpvZLYN8Z3yc9qio9YU8tQW5c1ELnh MWmTcOYtjUVHONlzYSxOQg4KuptrvjdH9PA6ibB2hCwzrPTYpGUNDUa62TPb SfIkV7PZwGkzcrU7LEqDpkn5KZcP92xtwRnw+lOl8wOZW09+UDtqh9i/0jkx ZrMkq9fYqsoPqD9A8zT4boHUSNz6e91uB5Qe5o5a+yphTGR4fiFyJ9JK5t3f jylj3USiaCP1LZR6n+OPJBVsKey4yvV3xlpeWIKXhRpYW89OjPB2YUh63kez WR1vt29LcYt0xa7h/UfOxC6F44OlEbIcN7gN8S2NjDRwOmV0UeyxB6O3Oal/ 12iCwRqNFbi6Y4NO32rHfVoo47F1TwV4QIOUsgenP0Ogqc9AhJ8nnMaZMhNv bbSxbvRw93vhYWuIMtNKB/a6L346cMgb1062BdKlOqCxI/hUnA/C1OKfi0S6 aLnoX5+W5ovguMPXaEV66G66NJuX6ocvwy1FruzPkW2Xb3Ap0R/3da0047ct h571WLA4k4mm2rRiKxV9xNrl9cuOB+CwssWezif6EM8UJJAFe6ExmOQcLfwC msccJrJKWRiuYuSXJBvgjqPN6fbiQOSbr1Bt9F4Bzbx0X7PqfeAXhbWz6Ybo 98les8MrCMx8loj2yhBafeWfUt1BmNlZKS9pWYkG3yhVU182JMMOCa2Zq9Bc 5XX20QM2ynZsXNnFXo1y5XFbOouDmox4nfD1RqCtL4sLGuQg0zvYRUVqBEO1 Sn0T/2BsGSy9ktlljNTHfj2858EoXFdc0+VCh/NX5vRbgSE4ejOn0KWRDu3K nzMuvgrB7pXelfdMGWgz+8F7ISoU30S3B+hkMVBgE9jo/SYUJas4pp1SBvw8 ZZvIg2EwvX35nFuACczTf3EwmQoDf32rhbjFBMf7rzSdiA5H2LRqz10LAgxX pkuyNByc+il6Vh6BpxamMdyDFCLTPOd3/Ujg68t7bwniKcR7CvtpZwlcJQr0 ug9ROCmNz+WfIzC0Sv365mQKtdvkc+cFBHjar5UW0ynIbyn6qqo//uerz/DP UeCLaTlt7QQuDG9quNZIoag8ijpxl8BcSOTS100UynkiR+cOAoeGKpiGLRQa 9PmzHSICQslyRUorhUGmHtX7DwEniczJuYOCmWSF40sJgSf/Nj16PEjBWphk VDFMoDH8vaXWMwrbMwbkoa8I/PraKoV8QcHVTHB1ZJTAo1GBScUwhTgu3ejd OwIuk0e5URMUku2OyX+bJiCJvd5cMkkhQ+vlA56UAH96cpl4ikJhXXn2zAwB GxlbuFVGoSxVNfzGLIE1iUXqEXIK1e6hDsnzBKznxH7FcxSEJndW2y8S2HNE s7prgULL9Fq5QkEgW+G4oFBQ+A9TLziI "]], LineBox[CompressedData[" 1:eJwV0vk/1HkAx/Gxjm0dlcRKxZevmkIt1bY69H1Hu1lX5T4iM4P5YCiiXKlE siVTkSuL0OVBaUcbYkvJShRKBz1KUqEiGtO4ZtsfXo/nP/DS5+509P+OxWLZ f+t/8+K5SmZ+Rzd09u8paZAPYu50UHZuVCCjORRVEbRFxMju1h2iqGim47ok 9kX+TSbvZqqeIpXC8E4ci2i68YARWESGSPSyGcEZ3Ww69iXTMUHSh/UuMot2 23RmC4aY77tesz/qVTH8yaXP1ANlTOG9/LBBvSamRn86xZTMQvnllC7B8ufM RoWBIVVvCnymLftDeC/zYMtgbdmWJQjtW9orKu9nMt5eclypZgpl/UT2S/Nh JsN2Zq325lU4PrvZqNB3lHm81n7snrk5uF3O/8jfH2MaqjGmuH89whoSuTvZ 48xyY8rknDtQsUvVSfv3KSbr79V/Xba3RGFs8ICpGwtDEzqZU4JNSMif3Pbl gxwsZ8e0mpHfwOp4hRsx8rh7tflKsIc1FkcERDkbKULD9tSn/ggbvBFnuqrU KqHYdk28g8AONn1B+06GzUBlz4xASaoDHN4IjXV1lTEzcWC63XErBm5zD/xb poJ6zkBYnt02LFfvXGi1Qw2Hojhz/vByhDIj5nSPzkQ527Ur0N0Jmz96Sgxc ZiPDt7otOMgZT+v95DxN1FE6t+fMrr0uqDxyx4cSq8OYFygk4a4IUIx81do6 B5kFHhUJCW7ghcdWquZoILy2YDztgDt+4hu32nHmYtoiXbsg2gMP5pioRK7R hJfZB157sidqyhNyTeS1kGmR9kRyyAuxckZb77/QwlNpRhSTsR3K3THWoaIf MXbQ8lNKoTf6zumn58dp48ymFccac32QvmSeQpXLPLSkJbqxS3dAmBPQyKF0 YOp2dJGFsy88071bVd/pwKez6Afy0BdfN5VI8+vmg+UeomDoxkFvn2VUffIC yJ13PvXsEQdnLczmt3AWokfuoznlzUVZUqQ6f5kufl12Nty3m4tkF56tvFgX DoolWgYePPzcXXgxuUUPFc/d2yJe8ZC1NLesxZbCnl+WULd8/LD/ZmqWbRWF dSUXkv585wf7+S4l9wz1Mcje4zIV4o+NoY1e6in6qF7hU+Uy6I/8BVzD+2J9 RDtJVjK7A2B4+/xpBy8DWCdesjQYCYBwWb1Re50BCp5crDkcykfAqEJbkxGN 9XaetnFiPrgVI1RKGg2pkeHO4N0EggSnSZsTNFzPb7+VF0kQ6SR6onqKRjOd ofFwL8ERceRx4WkasgVK11fFEZSvkU5k5tHfPn/Pmk4kkN6SdZ4rpbFusvSk 8DSBsF019U4jjat9K69VVhHkFIWQw000NP0FM97XEBRFtFpZN9MQvin21Kkj uKYlHG9updHSqymLryfo9tQgHY9pcHolm62bCdi986xe99IYe1vz7Hk3gako Rre4j0Yb/4ux2kuCtUldUv93NBrem8QzPQR27Lwr/QM0RgbyDIr7CMKDKd3P n2nwhvcHh3wiiFt/UHp1lMZE2PXa/GGCJLXXjyLENC6MDs9qHyHIulx09OtX GjYSjmi1hODsAQV+9TiNDdE5SoFSgtJt/pZxkzSsJ9rdcycIRAZ3F26YpkH2 qZS2TBHUjS6WymQ0imRWUzIZwX8kVDxt "]], LineBox[CompressedData[" 1:eJwV0Hs4lQcAx3F3HiQySnIuXutwkvCsjcT7W8rcS6g4HXHcr4d3tIrMzLUT nXIWKRlSM3OnPUqHsCSchtQWParTeXrS1eUsh5q1P77P5/8vk8ffG6mipKTk 86n/rcjkadhFCFx8X37rkf9YQPaPM7z3M2JJnW6HgtG638mVW+IfGYyj5JWV OOlh0QBZ0VNEV2cUks/E1gYlpx6QCc5pie/p58jp2Au6nOLn5PhyjOgdvY40 5Sh5aBe/JzUnn7Je0zvJjZW8nIUiTVTdqUx5SR8kH3Y7u70pWovGpsLJBJuH ZE9qT0KewBLR5Oi5V5SUFNqz3t1wskeSzEra3viC5NOtGgYNHaDNzGFNO7wj S1tdjlfHuaBYf4hdFTpP9v9qzihl7wBvMqBbdfgf0lPF9oTroV1I+SOHx2ct kXIVH2oxxx0tybr+6zw+ktwLVuN5qV6oSo+fsd2vhCSeZ1d6jS+yKz/4LbxS Rs5hzdWfS/ZAafwxuo6pYsFyNFPfdS82pkYdCWCrg3+7w77pgT+eyUv36dzQ QF+rtHqbXyA8ZXHHz6RoQTLH3n90Zh98nwk30WjaMMoK8NyecQAzfbys2w06 sBzsU7ycC4KNwX0z10OrUGzt9dq3kANtUh42Na8HZfraiotqXHzzOvi9eaA+ JH8vCasqQ/BXb4RysLUBlu2mw0Qmoego6A9hyA3gXccLkkyEIko97bFEsgbO U7NzT6rCEE6ld+iWG8KmoHomPpSHLdGbJN5hn2G5tlfZwTQcd9dY66Q5GmE0 4c21R7JwXG/MPm+taozJRKcxRXUE0pXZe4YfGWPaUCR4y4+E9tQx96T2tSjR OhjBcoyC7DJTVJmxDgWrdp2fWIiCyNJErTPQBD4tjqncnmgIy6MGwhjrwfbf Xc/JjEGwiCvRfb4eI7R7yhccYrG4s1ZRKTZFbl7EUodKHKSyHUd68zdgdMLI z607DtXOdqYjYWYQ3RzzaBbEoyE3zSB6Mw28E80/Cz0TkB8Y7qUqp8E67qNx m3oitk5V1eWP0DEqC9zS9GciyqzON4x4MTBke7eWWZyE73uKyrw6GaDWBYgT OXz4mAbW3rFgIkzLYvn4mmR8nTTAMShk4kmUjVtWcjIqN/AshuVMjJe48Pj3 k2HRd+WsL8ccFxmHGs5tTYFwcy97TGyOJtuvtGRnUhA1rzY6yCbAX230hdli Cngtc4zCUwTOeKqeEu6jkJDt/8HzNIEWnUbvLw9QSPNvf6BbQuDu8AHtqSAK BfK0YuFZAnq7G3NZXAqNjorl0goCP/kHZYjDKShurty/XE/g6sGm2FfJFIRj ukX9AwRC+Jyd7gIK5TWJMXmDBIpsNVTenKRQkypxdR8i0DXb3F1STOGqsXBp SELALFXDafo0halgw5jxCQJPjrTYHS6jwJKauD6VEsjJ1qRfqqVg236MdklG 4Jpr65THFQrbcicVkc8JzKlxy9/+QsGbVdH8YoZAaH6rkdNvFKh4Bm12loDb Sa7uWCuFjO0/KFrnCWT6aN35rp1C7qqn91LlBK7rteWbXaVQ1lQjWFwkYH9a SzW2k0J1llr0taVP//a29ehdp1DvF7kj4wOBesOQzPYuCu3mt8xc/iXw4p7W 9mAxBfH8RsXKCgHW2TbFSjeF/wAsYSxk "]], LineBox[CompressedData[" 1:eJwVxXk01AkAB3A3b0wiiyRz+KnJJOFtuyR+301ZhqbkKCSM+xx+S1uRZB1J mFBJSUZq29xHPSUkJaURUu3S09K8XirlKoPW7v7xeR+2QLg7WEFOTo7/n/8v SRaoWARl2/l7ii8q1InJzgGWyx5WOJl+9AL7ZOVNculB628s1iHSi3IuTirs IjXyb9TSXqaSKvQvyy9V9pEl7TlMZVYWSdOLWVOQ94KMsk2I/so8R0o47+k+ uW/JgYWwws/Ma+RIgbwTLfcrqTo0yvnIbCZVLgvSZnJUUfaoNO49s5ucaLN1 mMjRQ3VN1lCU2V/k3fj2qIzsdQgl+859oMZIkSXn8x0bS8RITcYaq9+RQqZJ Vbe2FWjsNM6I1WeyqN7uiDjCDrmaj7ll/tPk/T+MWGe5WyEYcm9T7PlC8hTM T9j7bUfc/TSBkDNPflHYQc2lOaIulu620ukb6XfBZCAj3hlliZHj5nvkECPg tSSW85Fauug680EeaQdUl6+R7ILcwGu0HFbEzLq+ZE373VgbH3LQnasM4cMm y5oXbngze9ZT/Y4KOuvHxJtdPcCTRhzJj1ND7xR3z6FxT/DfiNYzGDToprjz tiTtxfg9QcrDKnWYdN+TvZ/ygpnWc0N7v2XIM3X+yM/yAY2cDRie1oACU6/k opIvfv7o/dXIQxO9f86Lykr342VHkLy3qRYWLUYCCvX90XS8cz9rVgv8awIv yaA/QpQTXkskK2A7PDn1d1kAAqnEJnqxNsyOi8cj/QXYGLpe4hLwHRYqOuSt DALRu8JUPcFaB31RE7deSQNxuzr1vKmiLl5F2/TLxEFIlOfu6nmlixHtwuxP wmDQhg87xjTq4bTaviCOdQikV9iFpUkrkbVs+/nBmRAUrtNXavbQB7/OOt63 PRSi4pCuANYqcN12XvdJDoN3oa+E/nYVJIxn8heswjG3rUJW2mqA9Iyg+SaF CIxJtx7syFyNvkEdV4e2CIhtLQyeBBji9N1+p9rsSFSlJ2iFbmAg8ETtJREv Cpkegc6KswyYRnzTbVCOxqbhsmuZT5jol3psrHkajSKT81VPnFnoMe+tYOfG 4Gh7TpFzMwu/rHRvjfYRYoeBR8UjYzYC1IwXjqyIxU8xXT5aWWyMhpg5pMTG onS1wLhnlo2BAjuB8HksjO9dPcP3McJFll/VuU1xEG3o4Pa3GqHW/Ec1aX4c QqaV+rq5BGKX63xvOBcHQd0UKyuPQD5PMU/kSSEq1W2Rd4pAnXq1yw97KSS4 Nb6gFxB42rOXNuxF4fhsQq7oDAHNndXpHF8K1dayhbMlBE67eSW1BlKQ3V16 fuU6gZv7asI/xFIQ9dNzOrsI+Al9tjlmUygujw7L6CaQY66iMHGSQnm8xN7x MYE7k7VtBbkUbuiK5h9LCDDiVWxGTlEY9tYOGxgkMHqwzuJAEQXOmL796BiB 9FRV5uUKCuaNhxmXpQRu29cPO12lsDl9SBb8lsC0km/xp98puHBKat+NE/DP rNexqaRARbIYk5MEHE760vvrKSRtOSarnyaQskPt0a+NFNKXjT6LnyXQotGQ aXiDQlFNefbcHAHLU2qK4c0UxClKobfmCQh3N7Rr3KZw3TV4a9IigUrt/cmN LRQajR4Y2v1D4N0ztS3erRRap9fKlpYIcM40yJbaKPwLJGYxkg== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotRange->{{0, 10}, {-0.03650120481935486, 299.99999399329175`}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{{3.470311797530405*^9, 3.470311806158405*^9}, 3.470315064328637*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Energy", "[", RowBox[{"1", ",", "U"}], "]"}], ",", RowBox[{"{", RowBox[{"U", ",", "0", ",", "0.02"}], "}"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470311825776405*^9, 3.470311897139405*^9}}], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwVkXk4lAkAhx2lhNyDUo5W5OmQalUrPytlBh0bSpRyTLvG0bhzZRyVcR/f FKXUaFQG2SgM9TXRrMy3KCTVUqlsszzJunbDs+0f7/P+/74mficPMBXk5OT2 fON/2zhOjcarzu7ouvy4QVDDJ9VtmorrRf12k6E9ji0CPmnq3cJJEn2yK1y0 xeDtRT65NsQp0l/0jx17j8bFFWf45MZo5VAPkTKYQvup4sN8sjZOxtorMgA/ UkFWqsAnJ2a9PjmL1mDh3JjnoPs1Uteu0IIh2oZeLe7gzolSslF+KIfe6QzR vw5yM8sukl4WCYZBMjd4sE9daBYSZHvjqXdJrl6QMcaCKkU5pF/OMDOj5Dg4 xQ+14x1SyXFR2O7bff5Y3pMRwlsfRjp13dyq4/kzrMPN1sgSD4H30nOVcRsL JtoWtlRYAqYGh2OV5kIgv3d6l0djOtSGNcPON7FhsNDZVU6lALe8jV7RvMPR 6vY0uN/jAsTOgWLWeASMO62zslNLYFvNrfGpjELnMnphhfo12OcW95L0GHAt 0mKOVJbhxvskRfGiWDwZW5CpwClHRh2/ivcgDjbllveddt3CtPzd7L5DCfDY FPBM0i+EpOVydKP2aajfzR0xFVTDSDGat/hOEsrO1Z6dLK1BiHfBQHwjB91N Vi5Ni++AO37O6g9eMnTqRo7HsGrBoketiPJPQahm7zP1ujokvPh96VGHVDwf 3Tz9Vf8e3MxXXorXSkO72jX9PmY9fqnN+pA6kAZ1RolSh7AB1bEnNr9uOgPL 8OSiJWoiNM7brAzKOAuujqPA7WATJu9HqjqzzuF9md+zXlEzToo6G7R2p0Mw zB6N1n+A6ihTOS1tLi5VnUiDD4mVQW9cfL9wMfO37s3iYw/hZnTeevhhBjRn rAzWLxBDosHqO5iViTozjfJjAjFYtrc4tMAsXP+sssXY/RG6V79pVbXJRt98 4m2l6UcIcUlRc6PlgNRzOB99owXUesMvnR9zwGArMrVcWxG4r6fg+9pcSBT0 Dx8YbYVhb3xJND0Pm9tbebolj/HRV3nH6O083GU/H1oKCZ5kUoMqxvnIq2B6 nP0sgUvPFV+jnHwkjrhv55f8hg2zI1YdE/mgcytkczvasFbMVjALKIBe0JK5 pyNtyGSyTfSoAtREdL2Q5T759j3JaH5jIV6alZvf2dCOq+ktRtlXC3GFJ0sa ed0Og7bUkPpFBMz78zZFnpaiI6BLJ02ZwE/CH7buSpYiTX5F834VAs0M8XZa mhRj2+8tkS0l4FV6dFsDVwpJ1Z83DGkEgosGDWcJKcIL97xL/o5ApKpVYqpQ CspH75DrjwQMkmyv572QIuWr/7z+TgITogsBvq+ksCmqEXxwJLDXu9vUekAK /lPGxGk6gdD4kaLuISliHRPyf91HoJwmDKJ9lmK15VspzYcAh8cRXlpI4bVk XcTQMQLLR6cYwYsp5PvHLavxJcA+uf+jrQqF2RLtQAaTwEFBlf6ABoVu9d1K CcEEYit1A4wNKaRXFlTRQwmEWFV8GVtJwY4x6K7LJtBlvypRbEKhIuVUWXUE gSP1Ldl+5hSOGz12jo8i0Br1l9YmSwq6zZrjTjEE1MJmeIrrKLR7+hTrxH7r 1yuj9WygwJmssH8bR4Df8Yh33ZrCf1TkTvY= "]], LineBox[CompressedData[" 1:eJwVyXk41HkAx3FRoly5ajSZ6DDb6mCVauVTmuSobGG1LDWGZOyIXBnz5Cxj HIWfnhT7WIkUQ86M0RC5Gd8StZVSjvJoK0vbIbvtH+/n9cfbyPvEIV9FBQWF /d/6X0vWhzdRarM7HorTPhUOJcs0LeuzayWPrB9d/jeAU5gsM/ZojomWvLbW WqZRbhKYLDPl7Q3lSD5Z8+Mn/du+imRm4aqBrhJV+I2EP2evEMkq+RPcAxIa mO+7imc8hbLpWffXDpLvsNSqhWc1kiDTs85k2ku24drEaIeGskBWN+9lmp3c AVKBuIGytoA7U0APmHAGy2c5aOoCdNadehG9zx1nuytqzP4SwTtt3FeUcxTR ZCsj053ClCTYtmyQg9WajgvGyi9hb9+1rbqH/ZDtuk3tkDQPWX8eXrWynYsc 9QJzvnIBPjwbj1T+yoNN8Rryq1YR1MeXBF+oD8Kr++ryXJfrKPZgPNb3OIm8 LotMH49SNDn4N3GnQiAWJatompTDSpxU7lUShqcq/D3M2zex81z2A5ldBMYc F9ygba1E0Ui0UtPCSAhvtTl9kFdBVJVfmnWbjzxjWmGzVw3+mVedOugmgPee m2FBpBatzbnhdTqnscfAttbWuw4MpfAslYpomIef7vIflIDnkTEUVReD44nV mm1cKZKmEjc9zYpFyYxe7LuZBnDtwlaEceKAxzQy7iuD4GGPhqdNPM5YFUmX 8RvhbGJ4OUo7Aa4mk0saf2jC8cqU0fihBOw3puefed0EceQxiyf1ZzDSbprI F99B3ZylYYDoLDbGvDDUOdaMmYZQNQduIqY1v1Q/Nm3BCYn8lratEL4Hh5f3 v22BOMxYQVsnCZdDA+jCq3dhGPDckf0+Cetsk+wDua1wZlwwH28UQXGR0YCB cRtatbiDP6ckY1Mva776QBu4VsUx+v4pmPtctcU8ux331z5vUbNMRfD62drv nTrAc4xTd9ZPw4y2U7qbbie6N9Dfy8fS4El4fl7dnfB36s/YUnkOCsp1oTUx XaA/iMoJtzuPzSlrBneyujHGVt3xpuw84td7Mss+d6MjufvZ4pXpOHDDR92p sQeO/b+zGWnpyD0YRGPF9WLj7OSm3ul0VMmVNqy2lMO0KUhxjU8GOkZ5gs1f 5Ej2DTJa2p0BGxb7ksEvfUhiRjPmzDIxWlt2sr2iD3nCZkZqXiYygt1LNHQJ aO3xvNqFFIY+En5vIEGvT59ugiqFt7dvFHKCCBLmrZD+tJiCTQDz3sdggnfb axZNaFD4cWARc1UYQWvpqyK6PgXR+XB5RBTBycz9L2JXU0hxmVMzEhJ0ey11 27eLwt/HQ3aH/EEQ94Uzt2w3hdmiQY7KFQLLi+VXR1kUIiXD8bkFBPnEfvq0 HYWI6vE7bUUEkSxB+k0nCorxDVZ0McHadcNd+l4U3h0pYNyVEDxpXR/y8giF nrig7e5SgnQO36CcTcFw5KXL2waC2Rwdf3vfb7++UUhrIrivaass+I2C1Mx1 ktdGICzJKLULpFAv8Zyv1EFgbf/MRS+IwlMLDfrFToLrcaeuiEMo7HL1c7jT Q3CUcdchKozCgIkW201OoCddMrU3gsJGFjtiso+g87BXtm4kBU6je2rsPYKY mes7h/kUoipm8/X7Cf4DnqBPkQ== "]], LineBox[CompressedData[" 1:eJwViXk4lAkAh1GrJiLXUGGki7aS0pLFz7ZiZlRaR66yuSojRa4Gi1C5hvBp KbWWSsqtgxFjUhpjYnzDo1Khkqi2mqQDs2v/eJ/3eZ93md8R50AFOTm5HbP8 b3O7yXexytPWFpV5VPq3IJ6qeVPhLe4jm4IRY39Zy0GeoXdbYgJ3zKbemiqO OHGAtzbEIcKf+81G5R/Bxb81A3mmUZTDblwKDFipfRM/7+PVx4yzdnIXY2Tj 1Oj+BiZvYtprjMk1Bv1L6mBxpzu0bPKMGNwtYNyx0HH9KxqN8i+y6N1McJRC SzfVceBlFKcbPO4Cg2/Xipt6z0DYeOx5wnYvtCoFfnBLuAC/rNHA9KJ9mDFs qB72KIWUG2Zf3e+Pojc0piutDA7iKxaaHgfgpH5ZaWr1NeQ/9lhuIGChw3PJ /PvK1ZgcHGUrzoRAaq/oEr6zFgtH1cLONIXC2JFSITWtR7k3bYDqfRS9XrEt I2PXwWcG8VnScNR0PzWScm7CqiqtxqciEu8rt6mbMBpgm13Yx6NHI9j1fsH1 gUaUvUyYw5/HhuG/3+W3nWhC+vWSyvyWGHDyFv/RoteML/I3OP3ucYi3SjUT 5bWgve18VKNGPCRJe2Zq1FpBmxOVP78uAT2XNnkOdLQixDv3WWxjIvS+u5sc yOYjTXpqw9P846jLj59pcroDFj1SL9I/CWe1ZXwFhTbEPXygsndrMrIJ/snt d9rgslr/XKx6Ci75jAs1Iu/iYH3mSPKzFGSxbXval99DFXu/2ZOmE9jxmB7X MXQPjTJz/eD0k9gbtS1TcLodn5sjlJmsU5i4KscxdbqPI9zuBnX7VATEUdYP UASoijSUU9dIw4pdR/vv3hJAP3jI0fdjGvwCu0rMIjrgQjuzcbQ1Hfx1Xgdn lgvRvojVvzszAxnty/wsxUKwrMoTqUGZ2Bxru1AloxOSVUN3lc052OwSmeO8 RYQQx6SFLtQsbOIWRmyeFEG0Xvdj96ssuJduyM+9/ABBTr25P9VnIzksOT7G pQu6fbFFUfTTGHNdun6Bajde+VKs31WfRtknNXfdlm50ZIgGlQxyQK6IePDO WgzH3gu+tKwcKClUh2mfE8Nk+u2Grokc9PiyqXOlYqzlhyqsDMjF0NSqEuau HmQEhi7TFuXiK/6sdL3SgzSjBJrMNA+W7190lst6UJzaRuMU56FMUXbWew+J xYLkkFvzCLT+eCVDXE+iK0CsmUIh8PCtQN/9BokUeb3bu5QIzAxH1z29SeKD 5c0F4yoEwm8kDow3kmivfF2mSyVQoWNr9kMriaN5O54fX0FA6HlSzlJEQuSj 7b79FwIvR2rnXnxJImnKX6bzK4Fmp+byNa9ImBfUXBqxI7DRwtOpdpRESQ9j Ip5OwEO4tahlnATbLi6n1onAeN8zq0cfSKxaM9xJ9SHw5hCjUGWGxJP2deEv ficQ0BbgkC8jkeMfs6TGl4BbmdrkUjkJpos0ghiBs9/TwM14jgQSVXvFuEME XE00lthRJEityK2kHyag03RbJFwggQ1j0FUrlEDQ7q8JvylLcDXpWGlVOIGC qZWvfVQl2Ee7x4yNJOC8Uuf8yCIJtG6rSR2iCTheKHI+pC6B0MOnUJM921H1 8z9pSJD4+artcAwB1eY9PLaWBP8B6b5RnA== "]], LineBox[CompressedData[" 1:eJwVxXk4lAkAB2B0WJtuja2YkRIdS9oytU/Nj5oYUzFFuTZyFTON+6ZoKIMx DB9lt0Ry5ipKM5WSI0mIcXxWCVu2IstDPSLt7h/v865z8T7qrqSgoHD4P/9P Z34eDVed3Rt7tdCSwzNnLKXfz6iSkYwT9SbjO47oQtuhNipS9p5RkXe27huH jq18swBX2TRDL4b5vZ1jBsMgFa9jMhW4jv3SFMWxQUXYB66FbDXaZ/PGXCxP Y3LW/j1btgnZojmD9+xgrGKk6pnLdkP7q9OUBz0WUsUhMauVjQXTfI/B4kuw 14vQ4H2wwjTKYi8WZqFJGjIYecgelm1rdY/m34CLeNg9/spJhBAsffqjAkzI fE3Lul1RZv577pnYYpi1FexSsz2N7k9JKRZHypHWa7teq5GLr0qKM6M2t/G5 fzh04Tc+DmgWWdsxKrF4eLlv+n0fGB7Zb5DJuYtCB9qfFAc/yD929arvu4ca tmcNd8Ifp9KZC3q2yLCnNK7csTgQ1yq94lgmD2CclNH5iBUMfoiF1sMd1cj/ K3JejXIoaj9NKA1teoz4yusladVhmIoXtm7ZWYMvincSu20ioEO1k883eIKG 2qtB0pXnEBNh7JTEqAVtXlDaD7cjcVl/eiJkTx34Dimvw6VRWEJNZi/m1CNu Inbbq7Tz8FYNUJnv1AAuK1Az0FUA1XidKOpvTxHR82LJiX3RiFHevZH0aoSV LvWP8BUx+K7aOHjV+xk8KkRvo1/HYJdR2VAyrwmload29N2/gJu8eenUs88h naNTefEXwRQa7rsU0YyphwGqbG4sLMYDNIokL+Ata723wlSIKFO+vDe7BaWB 2gorVsZBIPg603+tFVTem4PO43HIGOkrqbZrgxUtffvw43jYQ/GcX28bGpZx u4+LElAwqzlSZPsS3D2FURRPEZ7sfEspG3iJjo1v6lTpibD0ZTVInNvBPyhY bEURw6/KN9Z4pB3N+hrjre/EmJMuy27id8DTUp5iVJGEWll1b8dIBzQ6w68E sZKhHpSzuTBIjnfOKntHy5LhH+gmOfZFjmcJzf2LtCR41jzHaxF04qA805km lmB4vUBYt6gLBrMj21omJeh698ROnNCFrTU+SjpuKRiOYz/fQOlGgrvPOvXm FCQf/2ideKkbcXqRtDnDVCT6c954U3qQJaylJWalIm+68wAtqwerG6P5VcoE xoZ2R2ZqkWhxa1OLUSHweM7mcJ82iRhFzQecRQRM1reuXaND4p9f7/74YQkB A/1GadomEg0lf+drUAiIWgenRdtJ+KUeHjy/gUBFcF58OJNEs6O6zSETAozc plFbDxKCGde5n/YTKHR+3ZDOJUG/XJ77lklA9wQrS36GxPWX5pPnWARmpFRr ji+JUGaE5JYlgb6C9kdmYSQ2bh54TnEkEO7CzDcSkehr+Nl/yImAcODWhQAx CYlr2JpyZwIuBwLcbieTmL2y0tPcncAn9y/a+mkkOpaaLow4Q+BV5WSOTiYJ YXFKCcuLQM585QuuWSQY5v3Wq3wIPBXzT2VfJ1EkCMkp9SfA+2a0WTOfxEla PTs8kMCNqgxVh0ISqx4snzALJpBrwxm7fJNEk61jhlooAcdG+/auEhJRU0XG A2EE6ifv3VErJ/EvybFWrw== "]], LineBox[CompressedData[" 1:eJwVy3s81IkCBfBQose0qcQmU4SKLVrSWhy11jDEvc1edSk1MyZmvFnymCKP 8ggZP3Zp0mO9dzIjSTNUJiWVxrv60WWFlMSmyV2Kve4f53M+n/P9nM2skAMc 1UWLFgUt5P9t7Tj9Pm7FFzvWxTnFgRkuVlnXF9TJSPvO7dSqw5YBMPBuSoiX vbUvXi4qNQ4NhFkQ7We2bMa+drsla/ZtMCyiNIP/JdPEU5+CCbePYaiJHeO5 y3Sh9OAIS1ROQPnF6y1dtg1RM2xL9eoErLPP3eoi+w7nJ/ykfskZkKoMZTm3 0VHmKWw21C+E11a+XsAYA6HrjA3T56/isTT6VbybF4Ysbuxj95XDc43+7l3+ XnA2E9q0KcvxKrApbTjJCyt/kvvaUCowS6VYuNR7wXuTlErZW4FtZ36L19ru DU33Oy0VpRVIPaDQK1l6GHNL/JeVhFWC9s7w4ON7RyD2FHtS1UXodHxUye8/ gugq5QV3qgg+RcHzO2aPYHZaY1vsHhGi/iktybXwQfBFOesBT4TSOnfl4cs+ GGQm3jFuE0E9OSZn8uRRLHm4nNKffw2srFFOuvAY/NTyFRyqGGvruDNRFcfg lnp1V5+VGM0D786xbx6D+6ZTjXATw9Tizxrb9mPwutN/uTNaDGXXXyqTakyo ikwiVDvEOKO7rIgRwMTnRk3pd/YS7Nl3zsIhmondS434Zc4SjPEoD8xSmEgP 2u+iypDAo0FrfMklJsw3DpTH+Umgc3SDza1OJnYd1Ag5ni1BZbHZMz0bFvbv 2zsZ3yvB4adVXE0aC68a7ob6D0lAmTaf+8Rg4e5nPSOrcQkiaFZb2oJYuDEx WBM3J4HtmF346SssPHJdVNysXw3FTg/Kaw02DLIdrfsOV2NKFuYkfs5G9o3o zMjWatB+semVjLBxwHPXo0td1RBGqAVf/8iGicdiFXnvgpvl5dWu8sV8RGno 2JsFv3hruJ7mC8Gz+r9HFl8HLeHvxJY6X/BSfp9s//46hD9m3h38hbOwF6fr lS14e/metYf8MHzc/nZjTA3yeg8ZbmrhYfFsHvMv7VpMD4zGqM8FocAxa8N0 0U2sHF0dll8fCmbD1DcnD9xChTe1T9s7HKaZy6ZOKaWQ07ly3lQEjIaSONKC ethWpUl8RJEoqZlZXRhyGw7ZBT13nU/Arju8ONziLsqG49XkS2NQWy/I3Sho RPqNq9fy7sRCp3A7vz1Djv+q1GY+P8hH4WjdV4zoe2huuhglXXMKVFrHIT1+ E6hqUXka1+ORVnvmR92w+wjyFvTHSRNwolRe9JD/AGlTZ83/k3ca+Vu/T+Gm NIPnHLkxkp0IPUr3k6KTD8F/8ZRyZF8SVt3ZnzWe0QKGif6FOK1kvIvI7LRJ ewT/mnMjSf3JuEQ1sHJNfIyqmOOWL+tT4J+x22RnzhNI5631A9LPQKU/Ris1 qxWfbv+8gs47i3cfin6/fOUpQmRtt7ScUhG9ZMTIWKJAVaTBIq01aZhVjPe0 i9qgH/CHK/NDGj5uCNTJPdoOBjV/12hjOsxL0lobB9rR/BXvuee5DLip2U4k H+kAz7YiQZt7DuF+cVG6rzvQZfzH/RXWmTBvsbh3idOJINfElQztLEjlhX6f JjvRukPvQ9vrLDwJmaNbhXWB69Et2F2TjcBv9b+em+yCXk+cMMr5PBqidxYL Yrrxmqlp9158Hpnla8M0Z7vxKKN1YPmmHLj9e1v//pQeuHYXMalZOdAcfJmx jvIMO7+MmyuUOVidw1C/lfkMZvJQVSNfAd553Cwz0XmODE7o5vWtAsynN5iG FDxH2tZ46rxFLt4fP6thqfMCl1ObqJmXc0E3nBx/cOUFdFuSguqWEggI6Bw2 NSCh8G1fm6xJID9S4cTdQiJZZWPDP5YTWNlDryg1JvGnzc1lYxQC9A9NIZtN STRfe1Omp03gsXmN6npLEuG5+1+d3kJgRMByUHUi0eqz/qDbXgLfXpjQJbkk Ej+z53V+IDDYVZahHUjC+ldJyYgjgSdBL+cYwSSudrgoTzkT2G1aN6QIJxHj yM+p9iDw9tcdtffjSBhvH3yi7UPgDKkWIskk8bL5m4ihowQOWTPfvM8mkcOO /VrCJGCSZ80yFZD4IlzDdeEQKJK5HyzNJ9G1ykmdH7jwzzOgCS+RSBUJrjkH E+D0/XCfvELC3mXgp3WhBITTL/euLyZRmRj9W1UEgT6dKHtBOYlj1Af0uEgC yp7I222VJNY1rJ6inSBwunvcduU1Eo8P+RSsjSFwY7K3gS4mkfCp0mEwlkCr qoNdajWJ/wGVykEp "]], LineBox[CompressedData[" 1:eJwVj2s0lAkAhkmHLEnKkCOTLqJsSGtyad5psxqGsumitDIuYeRSUi7jrjIY mvGNsiFKixDpZkZtrEgSCrnf5kuKdYqotaFtf7znOc+P58er6x64z2uRjIzM 4e/7nzTrzxMRynM7ft/o+6ZwIBnLaFWZDyTd9MiAJQemKSlY61IbEy15T09y +yzevTcFhv67T3tIZun9+rGF8tUpMDmjGHBAogiZJxVrR/P4uBM+xtkjWQW7 wEPrrL3TMD135L2dxABHZ9OO8bgCqNPT9W0l5iirOuqmuUaETYo+zB4DCxi1 Hk/dzBCB0W7l45dpgXOepuNMNxE4nLcF/FBLNI5EvruWK0J1hvnGV2Y70Erx 396tm4H7Xz4ISw8zoHNhX3ak3iW4O2YIzF7vQnpZo663RSbEsmQqs8UOYY5s 97u52Zg+mFznKscCjzbDt67NhnGJ6dxpGgtqOo5hUyPZKDyY4Jt3lYWo6FHL os05uFy8wfrfQHsY3fXo4VfmIPSAz2yx6h6MxCupJnZdxZX2z7cVihyh/q53 85VVeTiiz9X2G3PC1nwvXknRdTSKQ6XR9kew7qO+sa5ZEdxTR72Sstywx0rc XXiuDFOSkzZlnR6w5tdWBjyuwO7Wwu0rnb0xJn+jq1zmPkQ9zuvWNHDgWey6 Vf0nMT4PjobJz/tDoVlods70IZaOLj+ZURWEZezI0hPBj1HkQu2luJxCjIp8 PpNegxo73xrOVDD+SRj7yq76C1a3eOWuJSGQzOfMLj78BIy0zI7HzLM4aMX7 ZWVvHQreRMvVKITBdkG/73rkUyTdvVYq+jMcrfblldmaz/BF9h6/8xAXq3Zt V5661Ij62uwz4hVReDt/aGs1rQlUuTOiJRXRSM0y3UdWvYC/i3AgQhyDyeSB gii3FvCmLhj3i2IRxFa1ehjVCg4zZHWIRxwW9gvk2XgJbtcLld9+jsen1M2G O1VfwWmjzpUItQRwt0ktmW2v4HMnZSR+IAF8iWkiV9iGW2HHt/VVnYN697ae cXY7xAs0Hb+k8zCfHVGKXdeBmUenle04F8CMuG3060wHAiUtlWo2iRjXD511 qH2NWyFrZdRW8PDiw/LpwPhO6PgNsdiTPPBtqHVNTl1womZsHa1OAitci7uH 0o16VU7nwZRkND9KZ8y1d4NjVRRD8U0BUafW8uZ6D9r0hp4o0/jIrQsbnfTs hT8rbqkTJRUTB8Ybzc360LRFe7Ll7XeXBC39Y7YPvnvbhWZ30qDC5qvSxf3Q 7ojIOsO8CLqmuFeVN4C3bMUdE2UX4RkhbFZgDeJZctOg0hoBDp9n1GepDIHV nsOmpgpgGZcb+jxkCEZzfxs3TwugIDhroPx6CIY1QYs2eAoxVbuGwaEPI9kr SFejSYjSSAtWz9Vh8PSjqQsm6XC2jFJ3+zaM3MRaKj83Hfm9ATZy3lKsaoj3 f6BA4HmerGvlUymaPVtXJigSqBvLMfJ5JkWC7OqHjkoEGizpsprPpfhocf+H MRUCxZ/i8s82S1Ff+q5Am0Igtnj9uFmHFKfSHaSx67/31Q2h96RSNLlqHLLf SSDmfpqoYl6KuK8eC5q7CJhMnfB2/yYF7XL5jRFrAjnr7c3VZElce2k7HcUk kOyn2n9yMYkwa67g9l4Ci4LL15sokdDbNPyc4kpA45PD3TJNEn31PwaTxwjw XezOH9MiIfAI1ypnE/CoYDov0yYxl7XC19aLgJYBay6ASqJtmY089wSBI4be 1lv0SCSWCEuZAQTcZk9RBjaSoNsO7lcP+v6vPOYd34DEzbjQ67eCCSz05qVM GJJwo9bZRYQQkNt7zzV7Cwn1h8undp8lgJuNxg7GJBqdXTNXhhHYNjG8aN6E RMzMTcZwOIFjGl/bS0xJ/AeNY6Tv "]], LineBox[CompressedData[" 1:eJwVyXk81AkDx3HSupOrSa1MabeILWIpy3wrZdBhkQ7HMIaNESmLHBmhMs7F T7JJRYQ0ZkiaGbsWkSvkjOSYUYoUltp2ydPzx+f1+eO9yfOMg/cKCQkJ/6/9 /6b7P05HKC5abL5WubaQm4fVpsLsKsEAZZ/pzp54YR60XeqjWYK3lELbMwN+ jXnQ96f+yhB8ppjska/ZOZQHwxC5ACeBHBb4M4v1MvmoCJ9kHhGsQ8Gl+eB5 Wj7mF53f2gp0IS/QXpG66g7WUDJ0bAS74SoKf//IrwB8SXGKdYctjMfuuEn5 FMFZJ1LTb9IRUtITwge776GFf17EOuSMBbX57ENyHBxT0zLZ6eOMkyyniaI1 HIhO17PHY52R2GW4VUabg3/JSoY2Qmew3zNLms040L2cz1Ld5gJJH5GCz2kO 4h3aNQtkXFGte+QoqZMD6tTm4y11bljusOyvyS5D1/7mkshhN3henx2LKCwD LTfgy/Z/3cCrJ1eYV5QhxJ5fkGFIg8E1HfenbWUorDoy73qLhsjr3sYaElxI x4WlfbjgjtQNpOV1xlx4pkx4J+R4YMvcMaf5m1yoV/l+Din2gOSL/JfhhVw0 jkwlMR564FpBlKX8fS70DGcqzDs9oMvXjTsg4GK++x/JD1J0TGdeOGney8Xl dfK5jn50FCsUNz9cxcOufUmGe87TwTgXdkplDQ+TTKUG/Ut0aOfV+LM0ebCr Vn33zU06uiwfKGbr8aDh/q3Zoy46qiJt8wdseSi5o9+naeaJoiLLX/RTeHB9 yvGVo3oiMdQ8SC2LB6WPBksLjp7ozeb9RbrFQxD1x+86/D0hyZ5NPVvOg/mk xbmLtz0xxC55EvCch/YddkqvZRnQqH9GldAtx5zgrFVZPwOvtXKn5PrLQc0y G+S+YiDZtbnPXFyOnCCpgPK/GRj9Pdc+7MNX18/MrFztBVap05SibAVybjwa F1K9cPl27sr03RWgRi/HNFV5oSPKYbLuxlc/kFwzluUNz42qt9f7PgC1s2iX +olT6HkzuD78m4fIHDyxeWMTEzLuySXdJnx8HJkIk17yRy7FyNbFuBqrJlTO XhUGoixaunQwqAbFLuQXJJdz+Mkluc6HUotaW99a5lwQfhrOUw0R1sGcw+bS SoPxs5VTqcrJx9iTmt1bYx2Kusz2Yc0XDbg7zpKqlQlDJvULt/jCEyQ8yLuf +Wc4XN09um5rNOOTZGVy//FILD77R3khqwWN9TdC+GpRqPns5VNn2gayVEim bDkLFjrjEq+ET+Hvkj4cwY9Gs9GlaZZHB9hzVwxeZl7EUHcJvzqqE0zr4A3B jBg0GJ9g0vEMkc+fKrnti4XHUnf4XuUuOG7Vuh6hGod7gbER1t1d8KlIehU7 HAdKq1N1ZHo3OGG/GA8JLyHLPmPlO3oP+F9MtfwSLqPgsPqOi5t7sfDHr4q2 zCv4o7X0kP1CL84IOh6pWsXjw0i2ypH6PnCCtSVU1di4lBMvGxjbDy2/0YP0 WTYaK4/1tTk+hyP56s6JvxJw2KE34QhpAI3KzP5jSYk4/d7q8GLPAJjmxdEk 3yTkOswMjOcPonvL6GNF02RITr2ZmfV6Af+DMascSSkIalLs3m0yhLbtmrMd r1PADk5UL/w8BF+7nnSTilTI2rWRKPyX0OyNyAmx/g2f7+mPKbOH8ZouZzFd 9hsOPmR0yxwcQXNi24jCxjTY5rk15SiN4mBPLp2ckoZ4hajw1uBR7Fh8Z9A+ nwZ94SY9xb5R6NcGrvjeKx2aCb/vZVLGkOgduGltWzrq3ycdGrw5BrYOi/zF MAPCVg7JY3kMt+Lrycm3MrBhG4sqdUqEdU2x/lUyBFzCPtEePRGh3atTPU6O AM2RMPBpFiFOckP1zwoECn40WqHRKsKM2UP5SSUCDcqhBaHtIjTef3NXk0RA pLL2nUmvCOcyDosufkdA8LgqrFIkQhtt7fFDewl0bTx/tXxJhJj/GF80LAm0 zB/18VwWwfQat+DVfgLlNUZmqpJi5D2zmY+yJoBdn16eXSlG2P7INJ4dgeSC zO8NFcTYsm2slUQjcPG/HZVlGmIMNf4QJHYnULisd8V9vRhpjPD1XDoB9znd k6s1xVjMUfO18SbAuq23FEAWo3u1lXTkaQLyGlYHtm8RI740/b51AAGfGPu1 w1vFoNiMHF0TSMCin/Y2WVeMkpjz+ZwgApYUVvK0vhge5AbbiGACgXbp7je2 i7GmWmWOGkpA1uau4WEDMVpO0LLVwwgkbftTaslQjOiFkj1j4QTC/+7rLTUS 43+TfkBT "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotRange->{{0, 0.02}, {-0.036503962330978745`, 0.6000580002361027}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Scaled[0.02]}]], "Output", CellChangeTimes->{{3.470311827731405*^9, 3.470311899247405*^9}, 3.470315064742637*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Plot Normalized Eigenvectors", "Subsection", CellChangeTimes->{{3.470312358639405*^9, 3.470312368704405*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"ff", "[", "k_", "]"}], ":=", RowBox[{"k", "/", RowBox[{"Norm", "[", "k", "]"}]}]}]], "Input", CellChangeTimes->{{3.4703127607705708`*^9, 3.470312812699955*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{ RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "^", "2"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4703142380796356`*^9, 3.4703142449276357`*^9}, { 3.4703142767176356`*^9, 3.4703143025326357`*^9}, {3.4703143358026357`*^9, 3.4703143585206356`*^9}, {3.470314794314637*^9, 3.470314864262637*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7CWPLVBKOOlgDxVwYLrm8mq10Toon8Ph0I4X v/ZW3IHyBRzS8jbqnt31AsoXQZOXQNMv44Bq/geYPTDggMrlQOMLoPFF0PgS aHwZND79/AcAY3JGxA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "0.036503967857063474`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQAWIQDQEf7O+sSq7prl1gDxVwgPAfQPkcDnEPrDpTX9+D 8gUcGFCACJq8BJp+GQdU8z/Yo+pnQDOPA8N8VL4EGl8GjU8//wAAzAE/tw== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 5}], LineBox[{12, 6}], LineBox[{13, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{14, 15, 16, 17, 18, 19, 20}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "0.013608276348795436`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7E+9SdWXf/XAHirgkHAu+BJP0l0on8OhbPdC AYZPzlC+gMPyAkajVR8OQvkiaPISDlEo+mUcUM3/ALMHBhxQuRxofAE0vgga XwKNL4PGp5//ANz4QUA= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "0.0031706345237301403`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., 0.7055406512876979}, {2., 0.}, {3., 0.04703604341917985}, {4., 0.}, {5., 0.04703604341917985}, {6., 0.}, {7., 0.7055406512876979}, {1., 0.}, {3., 0.}, {5., 0.}, {7., 0.}, {1., 0.7055406512876979}, {2., 0.}, {3., 0.04703604341917985}, {4., 0.}, {5., 0.04703604341917985}, {6., 0.}, {7., 0.7055406512876979}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 3}], LineBox[{10, 5}], LineBox[{11, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{12, 13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7E+9SdWXf/XAHirgkHAu+BJP0l0on8OhbPdC AYZPzlC+gMPyAkajVR8OQvkiaPISDlEo+mUcUM3/ALMHBhxQuRxofAE0vgga XwKNL4PGp5//ANz4QUA= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.0031706345237301403`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQAWIQDQEf7O+sSq7prl1gDxVwgPAfQPkcDnEPrDpTX9+D 8gUcGFCACJq8BJp+GQdU8z/Yo+pnQDOPA8N8VL4EGl8GjU8//wAAzAE/tw== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 5}], LineBox[{12, 6}], LineBox[{13, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{14, 15, 16, 17, 18, 19, 20}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.013608276348795436`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7CWPLVBKOOlgDxVwYLrm8mq10Toon8Ph0I4X v/ZW3IHyBRzS8jbqnt31AsoXQZOXQNMv44Bq/geYPTDggMrlQOMLoPFF0PgS aHwZND79/AcAY3JGxA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.036503967857063474`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{3.4703142457686357`*^9, 3.4703142804636354`*^9, 3.4703143598696356`*^9, 3.4703148022476373`*^9, 3.4703148328246374`*^9, 3.470315065075637*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "0"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.470315105705637*^9, 3.4703151064166374`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7Otvf2bxjp1oDxVw+LmGgd/M6ziUz+HQdyOg 3/P3fShfwKFs84z2EuGnUL4ImrwEmn4ZB1TzP9jPmgkCO+H2ofI50PgCaHwR NL4EGl8GjU8//wEAlDdhZw== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{14, 7}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0.1}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "0.036503967857063474`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQAWIQDQEf7CH0gf1QAQcI9QDK53C45ee/8d7ve1C+gAMD ChCByUPNkYDph/JloPwD9qj2wQGaeRwY5qPyJdD4Mmh8+vkHAA1FKo8= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 5}], LineBox[{12, 6}], LineBox[{13, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{14, 15, 16, 17, 18, 19, 20}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "0.013608276348795436`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7LtuBPR7/r5vDxVwuOvxIC/43F0on8Nh/e3P LN6xE/dD+AIOF7rmN74uvwDli6DJSzjcQtEv44Bq/geYPTDggMrlQOMLoPFF 0PgSaHwZND79/AcAW+hM8A== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox[ RowBox[{"-", "0.0031706345237301403`"}], TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., -0.6846531968814576}, {2., 0.}, {3., 0.17677669529663687`}, {4., 0.}, {5., -0.17677669529663687`}, {6., 0.}, { 7., 0.6846531968814576}, {1., 0.}, {3., 0.}, {5., 0.}, {7., 0.}, { 1., -0.6846531968814576}, {2., 0.}, {3., 0.17677669529663687`}, {4., 0.}, {5., -0.17677669529663687`}, {6., 0.}, {7., 0.6846531968814576}}, {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{10, 5}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{9, 3}], LineBox[{11, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{12, 13, 14, 15, 16, 17, 18}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7LtuBPR7/r5vDxVwuOvxIC/43N39EC6Hw/rb n1m8YydC+QIOF7rmN74uvwBVL4ImL+FwC0W/jAOq+R9g9sCAAyqXA40vgMYX QeNLoPFl0Pj08x8A/OhN8A== "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{12, 5}], LineBox[{13, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{11, 4}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.0031706345237301403`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQAWIQDQEf7CH0gf1QAQcI9QAqzuFwy89/473f96DyAg4M KEAEJg9VLwHTD1UvA+UfsEe1Dw7QzOPAMB+VL4HGl0Hj088/AM02Ko8= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{10, 3}], LineBox[{12, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{9, 2}], LineBox[{11, 5}], LineBox[{13, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{14, 15, 16, 17, 18, 19, 20}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.013608276348795436`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7Otvf2bxjp1oDxVw+LmGgd/M6/h+CJfDoe9G QL/n7/tQeQGHss0z2kuEn0LlRdDkJdD0yzigmv8BZg8MOKByOdD4Amh8ETS+ BBpfBo1PP/8BAO5cRH4= "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{9, 2}], LineBox[{11, 4}], LineBox[{13, 6}]}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{10, 3}], LineBox[{12, 5}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.036503967857063474`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{3.470315107264637*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "1"}], ",", " ", RowBox[{"U", "=", "0.01"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{ RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "^", "2"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.470314887325637*^9, 3.470314898389637*^9}, 3.4703149400346375`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7DeV/gh8qLLZDirgkF7X7hujWmgP4XI4zGyb 5Lk37CKUL+Bgs5/ZY2ffWyhfxEG8HVlewuE9in4ZB7syZPM/2DOgAgdULgca XwCNL4LGl0Djy6Dx6ec/AKg/Pz4= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.09394332395815391`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7Ku+qvJbTH1jBxVwCFywwKTu03x7CJfDISsr JODXrGdQvoCD9vZb+fdbha0gfBGH+SjyEg4HUPTLOBxHMf+DPQMqcEDlcqDx BdD4Imh8CTS+DBqffv4DAFpyRAI= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.13723099012657888`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7Ccdev5vwl0We6iAw/e3DuEmCzdA+RwO7Jp/ 9v7d9gDKF3AQ7Of3M4h7CuWLOFRrIMtLOHSi6Jdx+HkQ2fwPMHtgwAGVy4HG F0Dji6DxJdD4Mmh8+vkPAIx9SLA= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.16255275359442417`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7E9m2bzPcvWxhwo4PFSM+vdl1jMon8PBTNWi JOvffChfwMHuSpBqx56flhC+iIOFNrK8hEOjKrJ+GQfbfGTzP8DsgQEHVC4H Gl8AjS+CxpdA48ug8ennPwDm4EEA "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.20265213851202846`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7E8ExHXsWO5jDxVwiNnEnBY28RmUz+EgV8vX tWfySihfwOHGr4T6LvaJUL6Iw9diZHkJh6wVyPplHARdkM3/ALMHBhxQuRxo fAE0vggaXwKNL4PGp5//AD+dPoQ= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.20338699762515577`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7LlOKsbNXfDMHirgIDtN6LZUhDeUz+HwcdG0 S3M2X7eD8AUcpq+5GyKVEmwJ4Ys4HOxDlpdweF2PrF/G4dQ2ZPM/wOyBAQdU LgcaXwCNL4LGl0Djy6Dx6ec/AInTQug= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.30011687136139303`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7LltlsbOXfDMHirg8DbywsamOG8on8PhMtPy 8Hn7b9pB+AIOTxcU9FmkzoXyRRxaxJDlJRwe5CPrl3Hw80M2/wPMHhhwQOVy oPEF0PgiaHwJNL4MGp9+/gMAUyZDuA== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["0.3001169248222665`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{{3.4703148898906374`*^9, 3.4703148993466372`*^9}, 3.470314940657637*^9, 3.4703150651786375`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "0"}], ",", " ", RowBox[{"U", "=", "1"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{ RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "^", "2"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4703149605826373`*^9, 3.470314984936637*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.}, {3., 0.}, {4., 1.}, {5., 0.}, {6., 0.}, {7., 0.}, {4., 0.}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 1.}, {5., 0.}, {6., 0.}, {7., 0.}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 4}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{9, 10, 11, 12, 13, 14, 15}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["12.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 1.}, {6., 0.}, {7., 0.}, {5., 0.}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 1.}, {6., 0.}, {7., 0.}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 5}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{9, 10, 11, 12, 13, 14, 15}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["14.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.}, {3., 1.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 0.}, {3., 0.}, {1., 0.}, {2., 0.}, {3., 1.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 0.}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 3}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{9, 10, 11, 12, 13, 14, 15}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["14.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 1.}, {7., 0.}, {6., 0.}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 1.}, {7., 0.}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 6}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{9, 10, 11, 12, 13, 14, 15}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["20.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 1.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 0.}, {2., 0.}, {1., 0.}, {2., 1.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 0.}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 2}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{9, 10, 11, 12, 13, 14, 15}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["20.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 1.}, {7., 0.}, {1., 0.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 1.}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{9, 10, 11, 12, 13, 14, 15}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["30.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[ GraphicsComplexBox[{{1., 1.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 0.}, {1., 0.}, {1., 1.}, {2., 0.}, {3., 0.}, {4., 0.}, {5., 0.}, {6., 0.}, {7., 0.}}, {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{9, 10, 11, 12, 13, 14, 15}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["30.`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{{3.4703149693056374`*^9, 3.470314985682637*^9}, 3.470315065269637*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"J", "=", "0.01"}], ",", " ", RowBox[{"U", "=", "1"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"tmp", "=", RowBox[{"Transpose", "[", RowBox[{"Sort", "[", RowBox[{"Transpose", "[", RowBox[{"N", "[", RowBox[{"Eigensystem", "[", RowBox[{"H", "[", RowBox[{"J", ",", "U"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Table", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"ff", "[", RowBox[{ RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"2", ",", "k"}], "]"}], "]"}], "^", "2"}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"tmp", "[", RowBox[{"[", RowBox[{"1", ",", "k"}], "]"}], "]"}]}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"k", ",", "1", ",", RowBox[{"NAtom", "+", "1"}]}], "}"}]}], "]"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.470315002518637*^9, 3.470315003110637*^9}, { 3.4703164478340783`*^9, 3.4703164606583605`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7BnmCJnMPfrREirgoBL1Qi1UMsgGwuVweFlz rX2JoL8dhC/g8O8/CLy3h/BFHFhrkeUlHCxR9Ms4sKCY/8GeARU4oHI50PgC aHwRNL4EGl8GjU8//wEA2QU/kg== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["11.999999942129632`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7B2ulzYEyM+1hgo4LMpcUMKc/90WwuVw+BTp UzhvwTN7CF/AYVHLlLmybCpQ9SIOi2Q3RSPkJRxmKzrGIfTLOAhbrkhBmP/B ngEVOKByOdD4Amh8ETS+BBpfBo1PP/8BAHvJO0Y= "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["13.999999997106482`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7E9dnFsYID/XGirg0DjvWipz/ndbCJfDYbrs puh5C57ZQ/gCDh+43ssJ/0i1g/BFHD5H+hQi5CUcpj0zrUHol3G4k5/dizD/ gz0DKnBA5XKg8QXQ+CJofAk0vgwan37+AwCSP0IU "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["14.000000054976852`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7KPYX9yZX7zSFirgMOfXfyB4bw/hcjj0SWVm fpzIYAfhCziwnur7myygYAPhizjckV3dscluM5Qv4TBzXjaz2dRFUPUyDj+W vWrJ64+1gdnHgAocULkcaHwBNL4IGl8CjS+Dxqef/wAhCEVq "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["20.000000002777764`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7L8ue9WS1x9rAxVwaJyXzWw2dZEdhMvhkNrP sHWX3WaovIBD8ZKdtctkFKB8EYcv0ZmZHycyQNVLOMz59R8I3ttD+DIOHuwv 7swvXmkLs48BFTigcjnQ+AJofBE0vgQaXwaNTz//AQAxsUXs "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["20.000000002777767`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7FFpBoefjQfuzC9eaQvhcji4Ok/Z6LC81xrC F3AQd323vHF/myWEL+LAk921k0WszRzCl3D4ubRpdYBiKpQv49DeyVGRPXGV JZo9MOCAyuVA4wug8UXQ+BJofBk0Pv38BwC2Kzny "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["30.000000000115737`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}], ",", GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQDQEf7Ns6OSqyJ66yhAo4ZISuePFUMdUcwuVwqPOT 4JYRa4PyBRzcXN8tb9zfBlUv4mDvPGWjw/JeawhfwuFl44E784tX2kL4Mg4w e1BpOHBA5XKg8QXQ+CJofAk0vgwan37+AwDWMzjq "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{8, 1}], LineBox[{9, 2}], LineBox[{10, 3}], LineBox[{11, 4}], LineBox[{12, 5}], LineBox[{13, 6}], LineBox[{14, 7}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{15, 16, 17, 18, 19, 20, 21}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{0, 0}, Frame->True, PlotLabel->FormBox["30.00000000011574`", TraditionalForm], PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]}], "}"}]], "Output", CellChangeTimes->{ 3.470315003854637*^9, 3.4703150653856373`*^9, {3.4703164486181564`*^9, 3.4703164615144463`*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Single particle - multiple wells", "Section", CellChangeTimes->{{3.4703194710615835`*^9, 3.4703194793334107`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"Hsp", "[", "Ns_", "]"}], ":=", RowBox[{"JJ", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Abs", "[", RowBox[{"i", "-", "j"}], "]"}], "\[Equal]", "1"}], ",", RowBox[{"-", "1"}], ",", "0"}], "]"}], ",", RowBox[{"{", RowBox[{"i", ",", "1", ",", "Ns"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "1", ",", "Ns"}], "}"}]}], "]"}]}]}]], "Input", CellChangeTimes->{{3.470319517915269*^9, 3.4703195992353997`*^9}, 3.470319732209696*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Hsp", "[", "1", "]"}], "//", "MatrixForm"}]], "Input", CellChangeTimes->{{3.470319603131789*^9, 3.470319614650941*^9}, 3.4703197262240973`*^9}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{{3.470319607674244*^9, 3.4703196154300194`*^9}, { 3.4703197270601807`*^9, 3.4703197353450093`*^9}}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"Emin", "[", "Ns_", "]"}], ":=", RowBox[{ RowBox[{"Sort", "[", RowBox[{"N", "[", RowBox[{"Eigenvalues", "[", RowBox[{"Hsp", "[", "Ns", "]"}], "]"}], "]"}], "]"}], "[", RowBox[{"[", "1", "]"}], "]"}]}]], "Input", CellChangeTimes->{{3.4703196338858643`*^9, 3.4703196819326687`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"Ns", ",", RowBox[{"Emin", "[", "Ns", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Ns", ",", "1", ",", "10"}], "}"}]}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.4703196857590513`*^9, 3.4703197140648813`*^9}, { 3.4703197464261174`*^9, 3.4703198066211367`*^9}}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQBWIQDQEf7BlQgQNUfD+E5nA4a12fNm/BNyhfwGHFl+mz yx//hPJFHFb5RLyo2vYbypdwKIw5vXLPlT9QvoyDW6/R+ewJf6F8BQcZ3SCn b4L/oHwlh/8hLsJ8+TC+ikN4wNnZWltgfJh7YIADjS+AxhdB40ug8WXQ+Apo fCU0vgoaf/CGFwAGCFzl "], {{{}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 2}], LineBox[{12, 3}], LineBox[{13, 4}], LineBox[{14, 5}], LineBox[{15, 6}], LineBox[{16, 7}], LineBox[{17, 8}], LineBox[{18, 9}], LineBox[{19, 10}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{20, 21, 22, 23, 24, 25, 26, 27, 28, 29}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{2., 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{{3.470319780919566*^9, 3.470319807347209*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Many particles - multiple wells", "Section", CellChangeTimes->{{3.4703198131447887`*^9, 3.4703198205795317`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"NNN", "[", RowBox[{"Ns_", ",", "Na_"}], "]"}], ":=", RowBox[{"Binomial", "[", RowBox[{ RowBox[{"Na", "+", "Ns", "-", "1"}], ",", "Na"}], "]"}]}]], "Input", CellChangeTimes->{{3.4703203935618243`*^9, 3.470320450383506*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NNN", "[", RowBox[{"3", ",", "3"}], "]"}]], "Input", CellChangeTimes->{{3.470320453957864*^9, 3.470320472055673*^9}}], Cell[BoxData["10"], "Output", CellChangeTimes->{{3.470320462903758*^9, 3.4703204724477124`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"Ns", ",", RowBox[{"NNN", "[", RowBox[{"Ns", ",", "5"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Ns", ",", "1", ",", "10"}], "}"}]}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.470320487706238*^9, 3.4703204932107887`*^9}}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQA2IQDQEf7FFpBgcIJQGlOaC0KZQWgNI+UFoEQjfEo+pr yIfyZSD0gxooXwFCH+iA8pUgtMwUKF8FQnvMd0BzFww4oHI50PgCaHwRNL4E Gl8Gja+AxldC46ug8Qdv+AEAhvYijQ== "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 1}], LineBox[{12, 2}], LineBox[{13, 3}], LineBox[{14, 4}], LineBox[{15, 5}], LineBox[{16, 6}], LineBox[{17, 7}], LineBox[{18, 8}], LineBox[{19, 9}], LineBox[{20, 10}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{21, 22, 23, 24, 25, 26, 27, 28, 29, 30}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{2., 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.470320500014469*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"ListPlot", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{"Ns", ",", RowBox[{"NNN", "[", RowBox[{"Ns", ",", "25"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Ns", ",", "1", ",", "10"}], "}"}]}], "]"}], ",", RowBox[{"Filling", "\[Rule]", "Axis"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"PointSize", "\[Rule]", ".03"}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{3.4703205125157185`*^9}], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQA2IQDQEf7FFpBgcIZQWlOSD0h1IoXwBCz1gJ5YuA6QOG 16F8CTAdkMroCOHLgPlGFWpQvgKY/2GtJ5SvBOI3xFdnQfkqIP6BvUydjmju ggEHVC4HGl8AjS+CxpdA48ug8RXQ+EpofBU0/uANPwC2Dy0T "], {{{}, {}, {}, {}, {Hue[0.67, 0.6, 0.6], Opacity[0.2], LineBox[{11, 1}], LineBox[{12, 2}], LineBox[{13, 3}], LineBox[{14, 4}], LineBox[{15, 5}], LineBox[{16, 6}], LineBox[{17, 7}], LineBox[{18, 8}], LineBox[{19, 9}], LineBox[{20, 10}]}}, {{}, {Hue[0.67, 0.6, 0.6], PointSize[0.03], PointBox[{21, 22, 23, 24, 25, 26, 27, 28, 29, 30}]}, {}}}], AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], AxesOrigin->{2., 0}, Frame->True, PlotRange->{All, All}, PlotRangeClipping->True, PlotRangePadding->{Automatic, Automatic}]], "Output", CellChangeTimes->{3.4703205133258*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"NNN", "[", RowBox[{"25", ",", "26"}], "]"}]], "Input", CellChangeTimes->{{3.4703205250669737`*^9, 3.4703205473472013`*^9}}], Cell[BoxData["121548660036300"], "Output", CellChangeTimes->{{3.470320526081075*^9, 3.470320548050272*^9}}] }, Open ]] }, Open ]] }, WindowSize->{1904, 814}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"7.0 for Microsoft Windows (64-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 110, 1, 71, "Section"], Cell[680, 25, 536, 16, 31, "Input"], Cell[CellGroupData[{ Cell[1241, 45, 656, 17, 31, "Input"], Cell[1900, 64, 11984, 203, 240, "Output"] }, Open ]], Cell[13899, 270, 481, 14, 31, "Input"], Cell[CellGroupData[{ Cell[14405, 288, 365, 9, 31, "Input"], Cell[14773, 299, 5995, 104, 247, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[20817, 409, 154, 2, 41, "Section"], Cell[20974, 413, 938, 24, 72, "Input"], Cell[CellGroupData[{ Cell[21937, 441, 648, 17, 52, "Input"], Cell[22588, 460, 918, 23, 131, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23543, 488, 1029, 28, 52, "Input"], Cell[24575, 518, 1809, 60, 250, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[26433, 584, 157, 2, 71, "Section"], Cell[26593, 588, 265, 8, 31, "Input"], Cell[CellGroupData[{ Cell[26883, 600, 110, 1, 36, "Subsection"], Cell[26996, 603, 400, 11, 31, "Input"], Cell[CellGroupData[{ Cell[27421, 618, 335, 9, 31, "Input"], Cell[27759, 629, 12535, 215, 239, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[40331, 849, 359, 9, 31, "Input"], Cell[40693, 860, 12484, 215, 243, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[53214, 1080, 361, 9, 31, "Input"], Cell[53578, 1091, 13981, 241, 242, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[67608, 1338, 116, 1, 36, "Subsection"], Cell[67727, 1341, 203, 5, 31, "Input"], Cell[CellGroupData[{ Cell[67955, 1350, 1708, 43, 112, "Input"], Cell[69666, 1395, 5903, 128, 155, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[75606, 1528, 1521, 40, 112, "Input"], Cell[77130, 1570, 6067, 130, 149, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[83234, 1705, 1583, 42, 112, "Input"], Cell[84820, 1749, 5822, 123, 151, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[90679, 1877, 1554, 41, 112, "Input"], Cell[92236, 1920, 4725, 102, 152, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[96998, 2027, 1608, 42, 112, "Input"], Cell[98609, 2071, 5898, 124, 152, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[104568, 2202, 121, 1, 71, "Section"], Cell[104692, 2205, 589, 17, 31, "Input"], Cell[CellGroupData[{ Cell[105306, 2226, 183, 4, 31, "Input"], Cell[105492, 2232, 684, 18, 44, "Output"] }, Open ]], Cell[106191, 2253, 343, 9, 31, "Input"], Cell[CellGroupData[{ Cell[106559, 2266, 719, 18, 31, "Input"], Cell[107281, 2286, 900, 18, 239, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[108230, 2310, 120, 1, 71, "Section"], Cell[108353, 2313, 273, 7, 31, "Input"], Cell[CellGroupData[{ Cell[108651, 2324, 145, 3, 31, "Input"], Cell[108799, 2329, 97, 1, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[108933, 2335, 692, 18, 31, "Input"], Cell[109628, 2355, 856, 18, 239, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[110521, 2378, 669, 18, 31, "Input"], Cell[111193, 2398, 870, 18, 232, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[112100, 2421, 151, 3, 31, "Input"], Cell[112254, 2426, 108, 1, 30, "Output"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)