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scheme 2

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Pierre-Francois Loos 2022-09-23 12:04:23 +02:00
parent 990a4dd960
commit e426497c82
2 changed files with 68 additions and 2 deletions
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4
scheme1.tex
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@ -17,13 +17,13 @@
\draw[-] (3,0) node[anchor=north]{$3$} -- (3,4);
\draw[-] (4,0) node[anchor=north]{$4$} -- (4,4);
\draw[-] (5,0) node[anchor=north]{$5$} -- (5,4);
\draw[-] (7,0) node[anchor=north]{$N$} -- (7,4);
\draw[-] (7,0) node[anchor=north]{$N = \infty$} -- (7,4);
% initial and final states
\draw[] (0,2) node[anchor=east]{$\ket{i_0}$};
\draw[] (7,3) node[anchor=west]{$\ket{i}$};
\draw[] (8,3) node[anchor=west]{$\displaystyle \ket{\Phi_0} = \sum_i c_i \ket{i}$};
\draw[] (8,2) node[anchor=west]{$\displaystyle c_i \sim \sum_{\substack{\text{all paths} \\ \text{ending at $\ket{i}$}}} \prod_{k}^{\infty} W_{i_k i_{k+1}}$};
\draw[] (8,2) node[anchor=west]{$\displaystyle c_i \sim \sum_{\substack{\text{all paths} \\ \text{ending at $\ket{i}$}}} \prod_{k}^{\infty} T_{i_k i_{k+1}}$};
% paths
\draw[thick,magenta] (0,2) node{$\bullet$} -- (1,3) node{$\bullet$} -- (2,2) node{$\bullet$} -- (3,3) node{$\bullet$} -- (4,3.5) node{$\bullet$} -- (5,3.75) node{$\bullet$} -- (7,3) node{$\bullet$};

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scheme2.tex Normal file
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@ -0,0 +1,66 @@
\documentclass[tikz]{standalone}
\usepackage{physics,amssymb}
\usepackage{circuitikz}
\usetikzlibrary{shapes.geometric}
\definecolor{darkgreen}{HTML}{009900}
\begin{document}
\begin{tikzpicture}[]
% frame
% \draw[-,thick] (0,0) -- (5.5,0);
% \draw[-,dashed,thick] (5.5,0) -- (6.5,0);
% \draw[->,thick] (6.5,0) -- (8,0) node[anchor=north west]{$\text{time} = N \tau $};
% \draw[->,thick] (0,0) node[anchor=north ]{$0$} -- (0,4) node[anchor=north east]{states};
% vertical lines
% \draw[-] (1,0) node[anchor=north]{$1$} -- (1,4);
% \draw[-] (2,0) node[anchor=north]{$2$} -- (2,4);
% \draw[-] (3,0) node[anchor=north]{$3$} -- (3,4);
% \draw[-] (4,0) node[anchor=north]{$4$} -- (4,4);
% \draw[-] (5,0) node[anchor=north]{$5$} -- (5,4);
% \draw[-] (7,0) node[anchor=north]{$N$} -- (7,4);
% initial and final states
% \draw[] (0,2) node[anchor=east]{$\ket{i_0}$};
% \draw[] (7,3) node[anchor=west]{$\ket{i}$};
% \draw[] (8,3) node[anchor=west]{$\displaystyle \ket{\Phi_0} = \sum_i c_i \ket{i}$};
% \draw[] (8,2) node[anchor=west]{$\displaystyle c_i \sim \sum_{\substack{\text{all paths} \\ \text{ending at $\ket{i}$}}} \prod_{k}^{\infty} W_{i_k i_{k+1}}$};
% paths
\draw[thick] (2,2) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (3,2.5);
\draw[thick] (3,2.5) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (3.25,3.5);
\draw[thick] (3.25,3.5) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (4,4);
\draw[thick] (4,4) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (5,3);
\draw[thick] (5,3) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (6,4);
\draw[thick] (6,4) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (7,3);
\draw[thick] (7,3) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (5,3);
\draw[thick] (5,3) node[scale=0.5]{$\bullet$} -- node[currarrow,midway,sloped,scale=0.5]{} (5.75,1.5);
\draw[thick] (5.75,1.5) node[scale=0.5]{$\blacksquare$} -- node[currarrow,midway,sloped,scale=0.5]{} (6.25,0.5);
\draw[thick,dashed] (6.25,0.5) node[scale=0.5]{$\blacksquare$} -- (7,0.25);
% states
\draw[] (2,2) node[scale=0.5,anchor=north]{$\ket{i_0} = \ket{I_0}$};
\draw[] (3,2.5) node[scale=0.5,anchor=north west]{$\ket{i_1}$};
\draw[] (3.25,3.5) node[scale=0.5,anchor=north west]{$\ket{i_2}$};
\draw[] (4,4) node[scale=0.5,anchor=west]{$\ket{i_3} = \ket{I_1}$};
\draw[] (5,3) node[scale=0.5,anchor=east]{$\ket{i_4} = \ket{i_7}$};
\draw[] (6,4) node[scale=0.5,anchor=south]{$\ket{i_5} = \ket{I_2}$};
\draw[] (7,3) node[scale=0.5,anchor=west]{$\ket{i_6}$};
\draw[] (5.75,1.5) node[scale=0.5,anchor=west]{$\ket{i_8} = \ket{I_3}$};
\draw[] (6.25,0.251) node[scale=0.5,anchor=east]{$\ket{i_9} = \ket{I_4}$};
% domains
\draw[thick,magenta,fill,opacity=0.2] (2.9,2.4) circle (1.5);
\draw[thick,cyan,fill,opacity=0.2] (4.25,3.25) circle (1.25);
\draw[thick,green,fill,opacity=0.2] (6,3.5) circle (1.5);
\draw[thick,orange,fill,opacity=0.2] (5.75,1.5) circle (0.45);
\draw[magenta] (2,3) node[scale=0.75]{$\mathcal{D}_{I_0}$};
\draw[cyan] (4.25,4.25) node[scale=0.75]{$\mathcal{D}_{I_1}$};
\draw[darkgreen] (6,4.75) node[scale=0.75]{$\mathcal{D}_{I_2}$};
\draw[orange] (5.6,1.3) node[scale=0.75]{$\mathcal{D}_{I_3}$};
\end{tikzpicture}
\end{document}