Non-Gaussian diffusion in static disordered media

TL;DR

This paper investigates non-Gaussian diffusion in static disordered media using a quenched trap model, revealing unique effects of quenched disorder, population splitting, and methods to estimate correlation length from particle trajectories.

Contribution

It introduces a detailed analysis of non-Gaussian diffusion in static media, including analytical estimates and novel mechanisms like population splitting.

Findings

Identification of population splitting mechanism

Analytical estimation of diffusion coefficient and fluctuations

Method to estimate correlation length from trajectory data

Abstract

Non-Gaussian diffusion is commonly considered as a result of fluctuating diffusivity, which is correlated in time or in space or both. In this work, we investigate the non-Gaussian diffusion in static disordered media via a quenched trap model, where the diffusivity is spatially correlated. Several unique effects due to quenched disorder are reported. We analytically estimate the diffusion coefficient $D_{\text{dis}}$ and its fluctuation over samples of finite size. We show a mechanism of population splitting in the non-Gaussian diffusion. It results in a sharp peak in the distribution of displacement $P(x,t)$ around $x=0$, that has frequently been observed in experiments. We examine the fidelity of the coarse-grained diffusion map, which is reconstructed from particle trajectories. Finally, we propose a procedure to estimate the correlation length in static disordered environments, where the information stored in the sample-to-sample fluctuation has been utilized.