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schemes done

This commit is contained in:
Pierre-Francois Loos 2022-09-23 13:36:51 +02:00
parent e426497c82
commit cf64f5d24f
2 changed files with 30 additions and 18 deletions
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21
scheme1.tex
View File

@ -7,8 +7,8 @@
% 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 $};
\draw[-,dash pattern=on 20pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 20pt,thick] (5,0) -- (7,0);
\draw[->,thick] (6.5,0) -- (8,0) node[anchor=west]{$\text{time} = N \tau $};
\draw[->,thick] (0,0) node[anchor=north ]{$0$} -- (0,4) node[anchor=north east]{states};
% vertical lines
@ -22,14 +22,19 @@
% 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} T_{i_k i_{k+1}}$};
\draw[] (8,2.5) node[anchor=west]{$\displaystyle \ket{\Phi_0} = \sum_i c_i \ket{i}$};
\draw[] (8,1.5) node[anchor=west]{$\displaystyle c_i \sim \sum_{\substack{\text{all paths} \\ \text{ending at $\ket{i}$}}} \prod_{k}^{\infty} T_{i_k i_{k+1}}$};
% paths
\draw[thick,magenta] (0,2) node{$\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$};
\draw[thick,red] (0,2) node{$\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$};
\draw[thick,green] (0,2) node{$\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$};
\draw[thick,blue] (0,2) node{$\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$};
\draw[thick,magenta] (0,2) node{$\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$};
\draw[thick,red] (0,2) node{$\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$};
\draw[thick,green] (0,2) node{$\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$};
\draw[thick,blue] (0,2) node{$\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$};
\draw[thick,magenta,dash pattern=on 22pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 22pt] (5,3.75) node{$\bullet$} -- (7,3) node{$\bullet$};
\draw[thick,red,dash pattern=on 20pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 20pt] (5,3) node{$\bullet$} -- (7,3) node{$\bullet$};
\draw[thick,green,dash pattern=on 25pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 25pt] (5,2) node{$\bullet$} -- (7,3) node{$\bullet$};
\draw[thick,blue,dash pattern=on 30pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 2pt off 2pt on 30pt] (5,1) node{$\bullet$} -- (7,3) node{$\bullet$};
\end{tikzpicture}

27
scheme2.tex
View File

@ -34,7 +34,7 @@
\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] (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);
@ -43,23 +43,30 @@
\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[] (4,4) node[scale=0.5,anchor=south west]{$\ket{i_3} = \ket{I_1}$};
\draw[] (5,3) node[scale=0.5,anchor=north east]{$\ket{i_4} = \ket{i_7}$};
\draw[] (6,4) node[scale=0.5,anchor=south west]{$\ket{i_5} = \ket{I_2}$};
\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[] (5.75,1.5) node[scale=0.5,anchor=south 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,cyan,fill,opacity=0.2] (4.25,3.5) circle (1.5);
\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[thick,orange,fill,opacity=0.2] (5.75,1.25) circle (0.7);
\draw[magenta] (2,3) node[scale=0.75]{$\mathcal{D}_{I_0}$};
\draw[cyan] (4.25,4.25) node[scale=0.75]{$\mathcal{D}_{I_1}$};
% domain labels
\draw[magenta] (2.2,3) node[scale=0.75]{$\mathcal{D}_{I_0}$};
\draw[cyan] (4.25,4.75) 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]{$\mathcal{D}_{I_3}$};
\draw[orange] (5.5,1.3) node[scale=0.75]{$\mathcal{D}_{I_3}$};
\draw[magenta] (2.2,2.7) node[scale=0.5]{$n_{I_0} = 3$};
\draw[cyan] (4.25,4.45) node[scale=0.5]{$n_{I_1} = 2$};
\draw[darkgreen] (6,4.45) node[scale=0.5]{$n_{I_2} = 3$};
\draw[orange] (5.5,1) node[scale=0.5]{$n_{I_3} = 1$};
\end{tikzpicture}