# moritz/spinoptics

[mpi] more slides

 @@ -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}