Thermally activated particle motion in biased correlated Gaussian disorder potentials

TL;DR

This paper investigates how a small bias influences the escape times of particles in correlated Gaussian disorder potentials, revealing an exponential reduction in escape times and validating predictions through advanced large-deviation simulations.

Contribution

It provides a theoretical analysis of the bias effect on barrier height distribution tails in correlated Gaussian potentials and confirms predictions with novel large-deviation simulation techniques.

Findings

Bias causes exponential decrease in mean escape time along its direction.

The tail of the barrier height distribution depends on the disorder's covariance properties.

Simulations successfully probe extremely small probability densities, validating theoretical predictions.

Abstract

Thermally activated particle motion in disorder potentials is controlled by the large-$\Delta V$ tail of the distribution of height $\Delta V$ of the potential barriers created by the disorder. We employ the optimal fluctuation method to evaluate this tail for correlated quenched Gaussian potentials in one dimension in the presence of a small bias of the potential. We focus on the mean escape time (MET) of overdamped particles averaged over the disorder. We show that the bias leads to a strong (exponential) reduction of the MET in the direction along the bias. The reduction depends both on the bias, and on detailed properties of the covariance of the disorder, such as its derivatives and asymptotic behavior at large distances. We verify our theoretical predictions for the large-$\Delta V$ tail of the barrier height distribution, as well as earlier predictions of this tail for zero bias, by performing large-deviation simulations of the potential disorder. The simulations employ correlated random potential sampling based on the circulant embedding method and the Wang-Landau algorithm, which enable us to probe probability densities smaller than $10^{-1200}$.