From 621112dcd660268bcb39189fd4ea06b712d864ed Mon Sep 17 00:00:00 2001 From: hebrewsnabla Date: Wed, 5 May 2021 00:54:32 +0800 Subject: [PATCH] #2 corrected --- chap3/GTO.nb | 7870 ++++++++++++++++++++++++++++++++++++++++++++++- chap4/chap4.pdf | Bin 90131 -> 90501 bytes chap4/chap4.tex | 4 +- 3 files changed, 7721 insertions(+), 153 deletions(-) diff --git a/chap3/GTO.nb b/chap3/GTO.nb index f251b9b..ffbbacd 100644 --- a/chap3/GTO.nb +++ b/chap3/GTO.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 1299995, 21743] -NotebookOptionsPosition[ 1299050, 21706] -NotebookOutlinePosition[ 1299406, 21722] -CellTagsIndexPosition[ 1299363, 21719] +NotebookDataLength[ 1746137, 29311] +NotebookOptionsPosition[ 1745060, 29270] +NotebookOutlinePosition[ 1745416, 29286] +CellTagsIndexPosition[ 1745373, 29283] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -7046,8 +7046,9 @@ yvE/DJC6qA== None, Evaluator -> Automatic, Method -> "Preemptive"], Alignment -> {Center, Center}, ImageSize -> Dynamic[{ - Automatic, 3.5 CurrentValue["FontCapHeight"]/ - AbsoluteCurrentValue[Magnification]}]], + Automatic, + 3.5 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], GridBox[{{ RowBox[{ TagBox["\"Name: \"", "SummaryItemAnnotation"], @@ -7135,147 +7136,7712 @@ f2N26fc= BaselinePosition -> {1, 1}], True -> GridBox[{{ PaneBox[ ButtonBox[ - DynamicBox[ - FEPrivate`FrontEndResource[ - "FEBitmaps", "SquareMinusIconMedium"]], - ButtonFunction :> (Typeset`open$$ = False), Appearance -> - None, Evaluator -> Automatic, Method -> "Preemptive"], - Alignment -> {Center, Center}, ImageSize -> + DynamicBox[ + FEPrivate`FrontEndResource[ + "FEBitmaps", "SquareMinusIconMedium"]], + ButtonFunction :> (Typeset`open$$ = False), Appearance -> + None, Evaluator -> Automatic, Method -> "Preemptive"], + Alignment -> {Center, Center}, ImageSize -> + Dynamic[{ + Automatic, + 3.5 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Baseline, DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + GrayLevel[0]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["GrayLevelColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + GrayLevel[0], Editable -> False, Selectable -> False], + ",", + RowBox[{"Opacity", "[", "0.5`", "]"}], ",", + RowBox[{"CapForm", "[", "\"Butt\"", "]"}]}], "]"}]}], + "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.3`"}], ",", + RowBox[{"Directive", "[", + RowBox[{ + InterpretationBox[ + ButtonBox[ + TooltipBox[ + 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"SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + GrayLevel[0], Editable -> False, Selectable -> False], + ",", + RowBox[{"Opacity", "[", "0.5`", "]"}], ",", + RowBox[{"CapForm", "[", "\"Butt\"", "]"}]}], "]"}]}], + "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.2`"}], ",", + RowBox[{"Directive", "[", + RowBox[{ + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + GrayLevel[0], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> GrayLevel[0.], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], "GrayLevel[0]"], + Appearance -> None, BaseStyle -> {}, BaselinePosition -> + Baseline, DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + GrayLevel[0]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["GrayLevelColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + GrayLevel[0], Editable -> False, Selectable -> False], + ",", + RowBox[{"Opacity", "[", "0.5`", "]"}], ",", + RowBox[{"CapForm", "[", "\"Butt\"", "]"}]}], "]"}]}], + "}"}], ",", + RowBox[{"{", + RowBox[{ + RowBox[{"-", "0.1`"}], ",", + RowBox[{"Directive", "[", + RowBox[{ + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + GrayLevel[0], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> GrayLevel[0.], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], "GrayLevel[0]"], + Appearance -> None, BaseStyle -> {}, BaselinePosition -> + Baseline, DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + GrayLevel[0]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["GrayLevelColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> 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CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], "GrayLevel[0]"], + Appearance -> None, BaseStyle -> {}, BaselinePosition -> + Baseline, DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + GrayLevel[0]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["GrayLevelColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + GrayLevel[0], Editable -> False, Selectable -> False], + ",", + RowBox[{"Opacity", "[", "0.5`", "]"}], ",", + RowBox[{"CapForm", "[", "\"Butt\"", "]"}]}], "]"}]}], + "}"}], ",", RowBox[{"{", - RowBox[{ - RowBox[{"-", "0.4218339392344389`"}], ",", - "0.4218339392344388`"}], "}"}]}], "}"}], ",", + RowBox[{"0.4`", ",", + RowBox[{"Directive", "[", + RowBox[{ + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + GrayLevel[0], + RectangleBox[{0, -1}, {2, 1}]}}, AspectRatio -> 1, Frame -> + True, FrameStyle -> GrayLevel[0.], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, 1.35 CurrentValue["FontCapHeight"]/ + AbsoluteCurrentValue[Magnification]}]], "GrayLevel[0]"], + Appearance -> None, BaseStyle -> {}, BaselinePosition -> + Baseline, DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + GrayLevel[0]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["GrayLevelColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + GrayLevel[0], Editable -> False, Selectable -> False], + ",", + RowBox[{"Opacity", "[", "0.5`", "]"}], ",", + RowBox[{"CapForm", "[", "\"Butt\"", "]"}]}], "]"}]}], + "}"}]}], "}"}], ",", RowBox[{"LabelStyle", "\[Rule]", RowBox[{"{", "}"}]}], ",", RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}], ",", RowBox[{"Charting`TickAnnotations", "\[Rule]", "None"}], ",", - RowBox[{"OpacityFunction", "\[Rule]", - RowBox[{"(", - RowBox[{ - RowBox[{ - RowBox[{"(", - RowBox[{ - RowBox[{"If", "[", - RowBox[{ - RowBox[{ - FractionBox["4", "9"], "\[LessEqual]", - RowBox[{ - RowBox[{"-", "1.`"}], "+", - RowBox[{"2.`", " ", "#1"}]}], "<", - FractionBox["5", "9"]}], ",", "0.01`", ",", "0.5`", ",", - "0"}], "]"}], "&"}], ")"}], "[", - RowBox[{"Rescale", "[", - RowBox[{"#1", ",", - RowBox[{"{", - RowBox[{"0", ",", "1"}], "}"}], ",", - RowBox[{"{", - RowBox[{"0.5`", ",", "1"}], "}"}]}], "]"}], "]"}], "&"}], - ")"}]}], ",", RowBox[{"Charting`TickSide", "\[Rule]", "Right"}], ",", RowBox[{"ColorFunctionScaling", "\[Rule]", "True"}]}], "]"}]& )], TraditionalForm], TraditionalForm]}, @@ -7296,9 +14862,7 @@ f2N26fc= RowBox[{#, ",", RowBox[{"Placed", "[", RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output", - CellChangeTimes->{ - 3.7896411605539618`*^9, {3.789641192467703*^9, 3.7896412144339724`*^9}, { - 3.7896412831851454`*^9, 3.789641299820676*^9}, 3.7896413822535305`*^9}] + CellChangeTimes->{{3.8168511180703325`*^9, 3.8168511428501267`*^9}}] }, Open ]], Cell[CellGroupData[{ @@ -21727,23 +29291,27 @@ Cell[1295, 45, 73486, 1199, 373, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[74818, 1249, 952, 26, 84, "Input"], -Cell[75773, 1277, 362727, 6023, 483, "Output"] +Cell[75773, 1277, 362773, 6025, 483, "Output"] +}, Open ]], +Cell[CellGroupData[{ +Cell[438583, 7307, 848, 24, 84, "Input"], +Cell[439434, 7333, 445076, 7531, 410, "Output"] }, Open ]], Cell[CellGroupData[{ -Cell[438537, 7305, 982, 25, 84, "Input"], -Cell[439522, 7332, 423997, 7011, 378, "Output"] +Cell[884547, 14869, 982, 25, 84, "Input"], +Cell[885532, 14896, 423997, 7011, 378, "Output"] }, Open ]], Cell[CellGroupData[{ -Cell[863556, 14348, 260, 9, 47, "Input"], -Cell[863819, 14359, 474, 15, 42, "Output"] +Cell[1309566, 21912, 260, 9, 47, "Input"], +Cell[1309829, 21923, 474, 15, 42, "Output"] }, Open ]], Cell[CellGroupData[{ -Cell[864330, 14379, 734, 21, 58, "Input"], -Cell[865067, 14402, 60570, 1073, 244, "Output"] +Cell[1310340, 21943, 734, 21, 58, "Input"], +Cell[1311077, 21966, 60570, 1073, 244, "Output"] }, Open ]], Cell[CellGroupData[{ -Cell[925674, 15480, 925, 27, 84, "Input"], -Cell[926602, 15509, 372432, 6194, 410, "Output"] +Cell[1371684, 23044, 925, 27, 84, "Input"], +Cell[1372612, 23073, 372432, 6194, 378, "Output"] }, Open ]] } ] diff --git a/chap4/chap4.pdf b/chap4/chap4.pdf index 53661031efbd63cce7948f422f0e02dbeb6ef405..1abcdcf8e1b8b59c67d7a0e5c1bcb292d3742465 100644 GIT binary patch delta 64740 zcmY(KQ*)pVkcB6@T-S}?7 zNpctsIO^X?74EAf>$s#9Wsf^WZRLkL_|m}RR6;z0i7`^zhbzP^Ok;TYt0ruIg_F!v zg5RiQq1Yl&VIuZ!UnHB;z~)vgtc(LcMlO*yGTM(U0%YBm?CSB!jr zzO>DjqE7P^oX*)1yYFP1qd;2_{Xted*6Q1BuE47Yk`LdH-<>GD3z_r-8T`|n$oS| zS^wG6!Oy8d0ZE`d9sZHOd~?5*+7owy#NZM5V6V@STl^s?lH1wd~UT*7m-D!Gxd$J;H}77eqd$^tV;#C89Tsq{S!6GX-rip!7u zGW-7aJb#~IwEYR`=^}NQEDg>Ju(Jya!n(P;T9`P%daqsT>%`-?q6ALYVISLI4$qil zOnWyYfnSgJ<`NhF~Igf#g7j^Z?SSXp_1vxE*!)ca@#cr@yEc=0tS zKPX+|Ut}ZnM{IuT*}kxSezFIA-5y?L3036Gfi{P2j!W4JP}3Bb5+Qv9ZE2_j2prNf zM!TA_V%v`)DREynin4NfX@pgNZ}1QBvUyoxykbS}Z(;mk&%(c@dN)VQf$k4M2boA? z`Bl{XoBT2c6(=Qt*+F5uw8mOU>0h$bwxjL**U=A5YsoT4P(!zK1lli#c`DH7U)%O) zD9ZsS1mS^7UHcas=ZShiJ@S6T#6LUTR9&Blmdu6=->cF4BD$W;oR>HB3D%l1rczZN 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-\lim\limits_{R\ra\infty}\Delta = 0 + \lim\lim\limits_{R\ra\infty} \qty[\dfrac{1}{2}(J_{11} + J_{22}) - 2J_{12} + K_{12}] = 0 +\lim\limits_{R\ra\infty}\Delta = 0 + \lim\limits_{R\ra\infty} \qty[\dfrac{1}{2}(J_{11} + J_{22}) - 2J_{12} + K_{12}] = 0 \end{align} \begin{equation}\label{key} \lim\limits_{R\ra\infty} E_{\corr} = -\lim\limits_{R\ra\infty} K_{12} @@ -272,7 +272,7 @@ \subsubsection{Intermediate Normalization and an Expression for the Correlation \end{align} As $ R\ra\infty $, $ S_{12}\ra 0 $, thus \begin{align} -\ket{\Phi_0} = \ket{\psi_1\bar\psi_1} - \ket{\psi_2\bar\psi_2} = \dfrac{1}{2}\qty(\ket{\phi_1\bar\phi_2} + \ket{\phi_2\bar\phi_1}) +\ket{\Phi_0} = \ket{\psi_1\bar\psi_1} - \ket{\psi_2\bar\psi_2} = \ket{\phi_1\bar\phi_2} + \ket{\phi_2\bar\phi_1} \end{align} Renormalize it, we get \begin{equation}\label{key}