Anomalous diffusion in disordered multi-channel systems

TL;DR

This paper investigates anomalous diffusion in multi-channel disordered systems, revealing how the diffusion exponent varies with the number of channels and inter-channel transition rates, using renormalization and simulations.

Contribution

It introduces a variant of the strong disorder renormalization group method to analyze diffusion in multi-channel systems with quenched disorder and explores the effects of symmetry and lane change rates.

Findings

Diffusion follows a power-law with an exponent depending on K and v.

Symmetric rate distributions lead to K-independent recurrent points.

As K increases, the diffusion exponent generally increases, and it decreases with v.

Abstract

We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong disorder renormalization group method and Monte Carlo simulations are used. Generally, we observe anomalous diffusion, where the average distance travelled by the particle, [<x(t)>]_{av}, has a power-law time-dependence [<x(t)>]_{av} ~ t^{\mu_K(v)}, with a diffusion exponent 0 \le \mu_K(v) \le 1. In the presence of left-right symmetry of the distribution of random rates, the recurrent point of the multi-channel system is independent of K, and the diffusion exponent is found to increase with K and decrease with v. In the absence of this symmetry, the recurrent point may be shifted with K and the current can be reversed by varying the lane change rate v.