42 lines
2.6 KiB
TeX
42 lines
2.6 KiB
TeX
\documentclass[tikz]{standalone}
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\usepackage{physics}
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\usetikzlibrary{arrows.meta}
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\begin{document}
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\begin{tikzpicture}[]
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% frame
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\draw[-,thick] (0,0) -- (5.5,0);
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\draw[-,dash pattern=on 20pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 20pt,thick] (5,0) -- (7,0);
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\draw[->,thick] (6.5,0) -- (8,0) node[anchor=west]{$\text{time} = N \tau $};
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\draw[->,thick] (0,0) node[anchor=north ]{$0$} -- (0,4) node[anchor=north east]{states};
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% vertical lines
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\draw[-] (1,0) node[anchor=north]{$1$} -- (1,4);
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\draw[-] (2,0) node[anchor=north]{$2$} -- (2,4);
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\draw[-] (3,0) node[anchor=north]{$3$} -- (3,4);
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\draw[-] (4,0) node[anchor=north]{$4$} -- (4,4);
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\draw[-] (5,0) node[anchor=north]{$5$} -- (5,4);
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\draw[-] (7,0) node[anchor=north]{$N = \infty$} -- (7,4);
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% initial and final states
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\draw[] (0,2) node[anchor=east]{$\ket{i_0}$};
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\draw[] (7,3) node[anchor=west]{$\ket{i}$};
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\draw[] (8,2.5) node[anchor=west]{$\displaystyle \ket{\Phi_0} = \sum_i c_i \ket{i}$};
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\draw[] (8,1.5) 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}}$};
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% paths
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\draw[thick,magenta] (0,2) node{$\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$};
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\draw[thick,red] (0,2) node{$\bullet$} -- (1,2) node{$\bullet$} -- (2,2) node{$\bullet$} -- (3,1.5) node{$\bullet$} -- (4,3) node{$\bullet$} -- (5,3) node{$\bullet$};% -- (7,3) node{$\bullet$};
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\draw[thick,green] (0,2) node{$\bullet$} -- (1,1) node{$\bullet$} -- (2,2) node{$\bullet$} -- (3,2.5) node{$\bullet$} -- (4,2.5) node{$\bullet$} -- (5,2) node{$\bullet$};% -- (7,3) node{$\bullet$};
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\draw[thick,blue] (0,2) node{$\bullet$} -- (1,0.25) node{$\bullet$} -- (2,1) node{$\bullet$} -- (3,1) node{$\bullet$} -- (4,2) node{$\bullet$} -- (5,1) node{$\bullet$};% -- (7,3) node{$\bullet$};
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\draw[thick,magenta,dash pattern=on 22pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 22pt] (5,3.75) node{$\bullet$} -- (7,3) node{$\bullet$};
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\draw[thick,red,dash pattern=on 20pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 20pt] (5,3) node{$\bullet$} -- (7,3) node{$\bullet$};
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\draw[thick,green,dash pattern=on 25pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 25pt] (5,2) node{$\bullet$} -- (7,3) node{$\bullet$};
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\draw[thick,blue,dash pattern=on 30pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 30pt] (5,1) node{$\bullet$} -- (7,3) node{$\bullet$};
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\end{tikzpicture}
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\end{document}
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