Diffusion with a broad class of stochastic diffusion coefficients

TL;DR

This paper explores how stochastic diffusion coefficients affect particle diffusion, revealing non-Gaussian, heavy-tailed propagators at finite times and Gaussian convergence over long times, depending on ergodicity.

Contribution

It introduces a novel approach to analyze diffusion with broad classes of stochastic diffusion coefficients, highlighting finite-time non-Gaussian behavior and conditions for Gaussian convergence.

Findings

Finite-time propagator is non-Gaussian and heavy-tailed.

Particles with stochastic DCs can diffuse farther than deterministic cases.

Long-time behavior converges to Gaussian distribution if the DC is ergodic.

Abstract

In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with a novel approach. We show that for a finite time, the propagator is non-Gaussian and heavy-tailed. This means that when the mean square displacements are the same, for a finite time, some of the diffusing particles with stochastic DCs diffuse farther than the particles with deterministic DCs or exhibiting a fractional Brownian motion. We also show that when a stochastic DC is ergodic, the propagator converges to a Gaussian distribution in the long time limit. The speed of convergence is determined by the autocovariance function of the DC.