Diffusion with a broad class of stochastic diffusion coefficients

Go Uchida; Hitoshi Washizu; Hiromi Miyoshi

doi:10.1103/physreve.109.064117

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arXiv · 2308.08820

Diffusion with a broad class of stochastic diffusion coefficients

Go Uchida·Hitoshi Washizu·Hiromi Miyoshi

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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.

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Go Uchida, Hitoshi Washizu, Hiromi Miyoshi. 2023-08-17. Diffusion with a broad class of stochastic diffusion coefficients. https://doi.org/10.1103/physreve.109.064117

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