Escape rate and diffusion of a random walker

TL;DR

This paper analyzes the escape rate and diffusion coefficient of a random walker in a periodic potential, revealing different behaviors in overdamped and underdamped limits and their temperature dependencies.

Contribution

It provides a detailed comparison of escape rates and diffusion coefficients for a random walker in different damping regimes, linking these to Langevin dynamics.

Findings

In the overdamped limit, the escape rate and diffusion match Langevin particle results.

In the underdamped limit, escape rate decreases while diffusion increases at low temperatures.

The dynamics show distinct temperature dependencies depending on damping regime.

Abstract

We determine the rate of escape from a potential well, and the diffusion coefficient in a periodic potential, of a random walker that moves under the influence of the potential in between successive collisions with the heat bath. In the overdamped limit, both the escape rate and the diffusion coefficient coincide with those of a Langevin particle. Conversely, in the underdamped limit the two dynamics have a different temperature dependence. In particular, at low temperature the random walk has a smaller escape rate, but a larger diffusion coefficient.