Kramers problem and energy diffusion

Abstract

The thermally activated escape of a Brownian particle over a potential barrier can be treated by the Smoluchowski equation if the high friction limit is considered. If the friction is weak, however, a different approach must be taken which is based on the concept of energy diffusion. The associated Kramers problem is to determine the rate at which the particle escapes from the potential well defining the barrier. In this work, through theory and simulations, we quantify the escape time as the mean first-passage time taken by the particle to cross the barrier by considering the energy diffusion approach