Numerical path integral calculation of the probability function and exit time: an application to non-gradient drift forces

Abstract

We provide numerical solutions based on the path integral representation of stochastic processes for non-gradient drift Langevin forces in the presence of noise, to follow the temporal evolution of the probability density function and to compute exit times even for arbitrary noise. We compare the results with theoretical calculations, obtaining excellent agreement in the weak noise limit.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Keywords: mean first passage time; nonlinear physics; path integral method; stochastic process; transitions induced by noise.