Duality between random trap and barrier models

TL;DR

This paper explores a duality between one-dimensional random trap and barrier models, revealing an exact relation between their diffusion behaviors and showing their disorder-averaged diffusion fronts are identical.

Contribution

It establishes an exact duality relation between two quenched disordered models and explains the physical origin of this duality through effective dynamics.

Findings

Discovered an exact relation between the diffusion fronts of the two models.

Proved that disorder-averaged diffusion fronts are exactly equal.

Identified the physical processes underlying the duality.

Abstract

We discuss the physical consequences of a duality between two models with quenched disorder, in which particles propagate in one dimension among random traps or across random barriers. We derive an exact relation between their diffusion fronts at fixed disorder, and deduce from this that their disorder-averaged diffusion fronts are exactly equal. We use effective dynamics schemes to isolate the different physical processes by which particles propagate in the models and discuss how the duality arises from a correspondence between the rates for these different processes.