Transient anomalous diffusion in heterogeneous media with stochastic resetting

TL;DR

This paper studies a stochastic resetting diffusion process in heterogeneous media, revealing transient anomalous diffusion, non-Gaussian distributions, and an optimal resetting rate that minimizes the mean first-passage time.

Contribution

It provides exact solutions for the probability distribution and mean first-passage time in a heterogeneous media with stochastic resetting, highlighting the effects of media heterogeneity.

Findings

Non-Gaussian distributions observed

Transient anomalous diffusion identified

Existence of an optimal resetting rate minimizing first-passage time

Abstract

We investigate a diffusion process in heterogeneous media where particles stochastically reset to their initial positions at a constant rate. The heterogeneous media is modeled using a spatial-dependent diffusion coefficient with a power-law dependence on particles' positions. We use the Green function approach to obtain exact solutions for the probability distribution of particles' positions and the mean square displacement. These results are further compared and agree with numerical simulations of a Langevin equation. We also study the first-passage time problem associated with this diffusion process and obtain an exact expression for the mean first-passage time. Our findings show that this system exhibits non-Gaussian distributions, transient anomalous diffusion (sub- or superdiffusion) and stationary states that simultaneously depend on the media heterogeneity and the resetting rate. We further demonstrate that the media heterogeneity non-trivially affect the mean first-passage time, yielding an optimal resetting rate for which this quantity displays a minimum.