Kramers's escape rate problem within a non-Markovian description

TL;DR

This paper compares escape rates of a Brownian particle in an asymmetric double-well potential under Markovian and non-Markovian noise, highlighting how finite noise correlation times affect escape dynamics.

Contribution

It provides a numerical and analytical comparison of Kramers's escape rate problem for both Markovian and non-Markovian thermal noise.

Findings

Finite correlation times significantly alter escape rates.

Analytical solutions match numerical results in limiting cases.

Non-Markovian noise introduces fundamental differences in escape dynamics.

Abstract

We compare the thermal escape rates of a Brownian particle, initially trapped into one of the two wells of an asymmetric double-well potential, for thermal Markovian and non-Markovian noise. The Markovian treatment of this problem goes originally back to the studies of Kramers in 1940 and is therefore often referred to as "Kramers's escape rate problem". We solve the generalized Langevin equation for the trajectories of the particles numerically and analytically for both limiting cases, Markovian and non-Markovian thermal noise. We compute the escape rate and work out the fundamental differences arising from finite correlation times of the thermal noise.