Analysis of self--averaging properties in the transport of particles through random media

TL;DR

This paper rigorously analyzes the self-averaging properties of particle transport in random media, revealing non-self-averaging behavior in subdiffusive regimes and providing exact calculations for directed walks.

Contribution

It offers a rigorous proof of non-self-averaging in subdiffusive regimes and develops a perturbative approach around EMA for symmetric random walks.

Findings

Transport coefficients are not self-averaging in subdiffusive regimes

Exact calculations for directed random walks

Perturbative analysis around EMA for symmetric walks

Abstract

We investigate self-averaging properties in the transport of particles through random media. We show rigorously that in the subdiffusive anomalous regime transport coefficients are not self--averaging quantities. These quantities are exactly calculated in the case of directed random walks. In the case of general symmetric random walks a perturbative analysis around the Effective Medium Approximation (EMA) is performed.