Transient superdiffusion in correlated diffusive media

TL;DR

This paper investigates how correlated inhomogeneities in a medium cause anomalous diffusion, specifically superdiffusion, by analyzing the effects of a random, time- and position-dependent diffusion coefficient.

Contribution

It introduces a perturbative approach to study the impact of correlated disorder on diffusion, highlighting the emergence of superdiffusive behavior.

Findings

Correlated disorder can induce superdiffusion in diffusive media.

Inhomogeneities affect the time scaling of the second moment.

Theoretical framework for understanding anomalous transport in complex media.

Abstract

Diffusion processes are studied theoretically for the case where the diffusion coefficient is itself a time and position dependent random function. We investigate how inhomogeneities and fluctuations of the diffusion coefficient affect the transport using a perturbative approach, with a special attention to the time scaling of the second moment. We show that correlated disorder can lead to anomalous transport and superdiffusion.