MOBILITY IN A ONE-DIMENSIONAL DISORDER POTENTIAL

TL;DR

This paper investigates how a particle's mobility in a one-dimensional disordered potential depends on temperature, force, and spatial correlations, revealing complex behaviors like non-Arrhenius temperature dependence and localization transitions.

Contribution

The study introduces a new framework linking mobility to disorder correlations and explicitly calculates mobility for models with spatial correlations, uncovering novel dynamical phenomena.

Findings

Mobility can deviate from Arrhenius behavior with temperature.

A localization transition from zero to finite mobility can occur at finite temperature.

Disorder correlations can suppress the localization transition.

Abstract

In this article the one-dimensional, overdamped motion of a classical particle is considered, which is coupled to a thermal bath and is drifting in a quenched disorder potential. The mobility of the particle is examined as a function of temperature and driving force acting on the particle. A framework is presented, which reveals the dependence of mobility on spatial correlations of the disorder potential. Mobility is then calculated explicitly for new models of disorder, in particular with spatial correlations. It exhibits interesting dynamical phenomena. Most markedly, the temperature dependence of mobility may deviate qualitatively from Arrhenius formula and a localization transition from zero to finite mobility may occur at finite temperature. Examples show a suppression of this transition by disorder correlations.