From cf64f5d24f6e61197fa7255b99703858cc0455d9 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 23 Sep 2022 13:36:51 +0200 Subject: [PATCH] schemes done --- scheme1.tex | 21 +++++++++++++-------- scheme2.tex | 27 +++++++++++++++++---------- 2 files changed, 30 insertions(+), 18 deletions(-) diff --git a/scheme1.tex b/scheme1.tex index 951a4e6..c029ca0 100644 --- a/scheme1.tex +++ b/scheme1.tex @@ -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$}; \end{tikzpicture} diff --git a/scheme2.tex b/scheme2.tex index 82cb358..4feabee 100644 --- a/scheme2.tex +++ b/scheme2.tex @@ -34,7 +34,7 @@ \draw[thick] (4,4) node[scale=0.5]{$\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}