Diffusion in disordered media as a process with memory

TL;DR

This paper introduces a memory-based model for random walks in disordered media, capturing effects like aging and localization without relying on specific disorder realizations, providing a new perspective on such complex systems.

Contribution

It presents a novel model of random walks with memory that effectively reproduces disorder effects without referencing specific disorder configurations.

Findings

Model reproduces disorder effects naturally

Captures aging and localization phenomena

Provides a disorder-independent framework

Abstract

The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of the two models implies that the new model retrieves dynamically a realization of disorder; the only one which is consistent with its dynamics. In this new approach to the dynamics in disordered media, effects of memory, aging and the peculiar localization properties of the random walker, appear quite natural.