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[mpi] more slides

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commit f462da54ce946632b8d0fd0f448437b3f94a5ed1 1 parent 6eba4b8
@moritz authored
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BIN  slides/adapting-pic.pdf
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BIN  slides/comparison-over-phi.pdf
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26 slides/mpi.tex
@@ -12,6 +12,8 @@
\usepackage{array}
\usepackage[normalem]{ulem}
\usepackage{fancyvrb,verbatim}
+\usepackage{amsmath}
+\usefonttheme{professionalfonts}
\setlength{\extrarowheight}{2mm}
\newcommand{\vect}[2]{\ensuremath{\inp{\hspace{-.8ex}\begin{array}{c}#1\\#2\end{array}\hspace{-.4ex}}}}
@@ -263,11 +265,11 @@ \subsection{Landauer Formula}
\end{center}
\end{frame}
-\begin{frame}{Theory: Coupling}
+\begin{frame}{Theory: Discretization}
Problem: $(E\pm i\eta-H)$ is an operator, and not easily invertible\\[1em]
\pause
- Solution: discretize derivative into finite differences\\[1em]
+ Solution: discretize derivatives into finite differences\\[1em]
\pause
Leads: Analytical Green's functions known\\[1em]
@@ -348,4 +350,24 @@ \subsection{Analytical calculations}
\includegraphics[width=0.7\textwidth]{critical-angle.pdf}
\end{center}
\end{frame}
+
+\begin{frame}{Adapting to $\uparrow, \downarrow$ bases}
+ \begin{center}
+ \includegraphics[width=\textwidth]{adapting-pic.pdf}
+ \begin{align*}
+ T_{2\uparrow,1\uparrow} = \left| \left(
+ a \mathbf{\Psi^+}(x=x_2) + b \mathbf{\Psi^-}(x=x_2)
+ \right)^\dagger \cdot \mathbf{\Psi}^\uparrow(x=x_2) \right|^2\nonumber\\
+ T_{2\downarrow,1\uparrow} = \left| \left(
+ a \mathbf{\Psi^+}(x=x_2) + b \mathbf{\Psi^-}(x=x_2)
+ \right)^\dagger \cdot \mathbf{\Psi}^\downarrow(x=x_2) \right|^2\nonumber
+ \end{align*}
+ \end{center}
+
+\end{frame}
+
+\begin{frame}{What survives...}
+ \includegraphics[width=\textwidth]{comparison-over-phi.pdf}
+\end{frame}
+
\end{document}
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