Diffusion in Modulated Media

TL;DR

This paper investigates the transition from localized to diffusive behavior of Brownian particles in modulated media, providing exact diffusion coefficients and analyzing effects of media structure on transport.

Contribution

It introduces a toy model to study particle motion in modulated media, deriving exact diffusion coefficients and examining effects of media periodicity and incommensurability.

Findings

Localized behavior with finite minima in potential

Diffusive behavior with infinite minima

Exact diffusion coefficient in periodic force field

Abstract

We study the motion of Brownian particle in modulated media in the strong damping limit by using {\em toy model}, with special emphasis on the transition from localise to diffusive behavior. By using model potential we have seen the localised behavior when the number of minima of the potential is finite in the asymptotic time limit. In the limit of infinite number of minima we have seen the diffusive behavior.We calculate exactly the diffusion coefficient in periodic field of force. We have also studied the transport in commensurate and incommensurate media.