Rectification and non-Gaussian diffusion in heterogeneous media

TL;DR

This paper investigates how heterogeneity in media causes deviations from Gaussian diffusion in Brownian motion, revealing effects like rectification and enabling characterization of local forces and medium properties.

Contribution

It introduces a theoretical framework for understanding non-Gaussian diffusion in heterogeneous media, validated by numerical simulations, and highlights potential applications in micro and nano-systems.

Findings

Deviations from Gaussian distribution depend on local forces and medium properties.

Theoretical predictions match numerical results in disordered and confined systems.

Deviations lead to rectification effects in diffusion.

Abstract

We show that when Brownian motion takes place in a heterogeneous medium, the presence of local forces and transport coefficients leads to deviations from a Gaussian probability distribution that make that the ratio between forward and backward probabilities depends on the nature of the host medium, on local forces and also on time. We have applied our results to two situations: diffusion in a disordered medium and diffusion in a confined system. For such scenarios we have shown that our theoretical predictions are in very good agreement with numerical results. Moreover we have shown that the deviations from the Gaussian solution lead to the onset of rectification. Our predictions could be used to detect the presence of local forces and to characterize the intrinsic short-scale properties of the host medium, a problem of current interest in the study of micro and nano-systems.