\documentclass[12pt]{article}
\usepackage{graphicx}
\title{Path Integral Monte Carlo}
\author{Keola Wierschem}
\date{October 2002}
\begin{document}
\raggedright
\Large{Path Integral Monte Carlo\\}
\vspace{0.5cm}
\large{a presentation by Keola Wierschem}
\newpage

{\Large Metropolis Monte Carlo}
\begin{itemize}
\item {\large based on random sampling}
\item {\large an exact simulation technique}
\item {\large error from approximations in atomic interactions, finite-size effects, and use of pseudo-random numbers}
\end{itemize}

{\Large Sampling Technique}
\begin{itemize}
\item {\large start with any configuration of particles}
\item {\large systematically propose and accept/reject new particle positions}
\item {\large must satisfy detailed balance}
\item {\large must be able to reach all possible configurations in a finite number of iterations}
\item {\large an iteration occurs when a new position has been proposed and accepted/rejected for each particle in the system}
\end{itemize}

{\Large Accept or Reject?}
\begin{itemize}
\item {large based on Hamiltonian of system}
\item {large ie kinetic and potential}
\item {large changes with temperature and forces}
\end{itemize}
\newpage

\begin{figure}
\end{figure}
\newpage

\begin{figure}
\includegraphics[height=125mm]{figures/freecluster.ps}
\caption{\large Initial configuration of humans}
\end{figure}
\newpage

\begin{figure}
\includegraphics[height=125mm]{figures/freespread.ps}
\caption{\large Relaxed configuration of humans}
\end{figure}
\newpage

\begin{figure}
\includegraphics[height=125mm]{figures/kegspread.ps}
\caption{\large Relaxed configuration of humans adjusted by KEG}
\end{figure}
\newpage

{\Large Path Integrals}
\begin{itemize}
\item {\large developed by R. P. Feynman mid-20th century}
\item {\large describe quantum particles as classical "ring-polymers"}
\item {\large use concept of imaginary time (inverse of temperature)}
\item {\large allow one to understand the quantum effects at low temperature in terms of the better understood classical behavior at higher temperature}
\end{itemize}

{\Large Path Integral Monte Carlo}
\begin{itemize}
\item {\large uses path integrals to reduce the temperature of interactions in standard Monte Carlo}
\item {\large more paths = lower temperature}
\item {\large has been used to study superfluidity, a quantum effect occuring at low temperatures}
\end{itemize}

{\Large Superfluidity}
\begin{itemize}
\item {\large A superfluid has zero viscosity, or resistance to flow}
\item {\large Helium is the observed superfluid to date}
\item {\large Bulk helium becomes superfluid at about 2.17 K}
\item {\large PIMC can be used to search for new superfluids}
\item {\large Using computer simulation, one can study any number of systems with very little cost}
\end{itemize}
\newpage

\begin{figure}
\includegraphics[height=150mm]{figures/fig2.ps}
\caption{from Ceperly and Gordillo: superfluid hydrogen on silver doped with alkali metal}
\end{figure}
\newpage

{\Large Summary}
\begin{itemize}
\item {\large Monte Carlo is a powerful technique based on random sampling}
\item {\large Path integrals, when applied to MC, allow one to simulate the quantum effects of particles that occur at low temperatures}
\end{itemize}
\end{document}
