Flux reversal in a simple random walk model on a fluctuating symmetric lattice

TL;DR

This paper introduces a simple one-dimensional random walk model on a fluctuating symmetric lattice, revealing how the direction of steady motion can be reversed by tuning transition rates and residence times.

Contribution

It provides exact explicit formulas for long-time velocity and diffusion coefficient in a fluctuating lattice model, demonstrating flux reversal mechanisms.

Findings

Steady motion direction can be reversed by changing residence times.

Explicit expressions for velocity and diffusion are derived.

Flux reversal depends on transition rates and residence times.

Abstract

A rather simple random walk model on a one-dimensional lattice is put forward. The lattice as a whole switches randomly between two possible states which are spatially symmetric. Both lattice states are identical, but translated by one site with respect to each other, and consist of infinite arrays of absorbing sites separated by two non-absorbing sites. Exact explicit expressions for the long-time velocity and the effective diffusion coefficient are obtained and discussed. In particular, it is shown that the direction of the steady motion can be reversed by conveniently varying the values of either the mean residence times in the lattice states or the transition rates to the absorbing and non-absorbing sites.