Driven classical diffusion with strong correlated disorder

TL;DR

This paper provides an exact analysis of the mobility of an overdamped particle in a disordered potential under arbitrary driving forces, revealing a non-linear regime with power-law behavior for strong disorder.

Contribution

It generalizes existing results by deriving an exact expression for mobility under strong disorder and arbitrary driving, including a novel non-linear regime with power-law dependence.

Findings

Mobility mu(F) is self-averaging in the thermodynamic limit.

Exact calculation of mu(F) for arbitrary disorder strength and driving force.

Identification of a non-linear regime with power-law dependence for strong disorder.

Abstract

We analyze one-dimensional motion of an overdamped classical particle in the presence of external disorder potential and an arbitrary driving force F. In thermodynamical limit the effective force-dependent mobility mu(F) is self-averaging, although the required system size may be exponentially large for strong disorder. We calculate the mobility mu(F) exactly, generalizing the known results in linear response (weak driving force) and the perturbation theory in powers of the disorder amplitude. For a strong disorder potential with power-law correlations we identify a non-linear regime with a prominent power-law dependence of the logarithm of mu(F) on the driving force.