Path Integral Solution of the Kramers Problem

Abstract

An iterative method to generate a discrete path integral solution of the Kramers problem is presented. It is based on a straightforward derivation of the functional formalism from the underlying Langevin equations. The method is rather simple and systematic and allows us to analytically evaluate the short time propagator up to and including terms of fourth order in a time increment τ. This means a significant reduction of the number of time steps N that are necessary to obtain convergent results for a given net increment t=Nτ.