DIFFUSIVE TRANSPORT IN A ONE DIMENSIONAL DISORDERED POTENTIAL INVOLVING CORRELATIONS

TL;DR

This paper investigates one-dimensional Brownian diffusion in a correlated disordered potential, revealing similar large-time scaling laws to uncorrelated cases but significant differences in stationary flux distribution.

Contribution

It introduces analysis of transport in correlated disordered potentials and compares it to uncorrelated cases, highlighting key differences in flux distribution.

Findings

Large-time scaling laws are similar to uncorrelated cases.

Stationary flux distribution differs significantly from uncorrelated case.

Correlations impact the stationary flux probability distribution.

Abstract

This article deals with transport properties of one dimensional Brownian diffusion under the influence of a correlated quenched random force, distributed as a two-level Poisson process. We find in particular that large time scaling laws of the position of the Brownian particle are analogous to the uncorrelated case. We discuss also the probability distribution of the stationary flux going through a sample between two prescribed concentrations, which differs significantly from the uncorrelated case.