Non-Gaussian Normal Diffusion in Low Dimensional Systems

TL;DR

This paper investigates the microscopic mechanisms behind non-Gaussian normal diffusion (NGND) in low-dimensional systems, revealing transient effects related to diffusivity modulation and introducing a generalized framework for understanding NGND distributions.

Contribution

It demonstrates that NGND is a transient phenomenon linked to diffusivity fluctuations and proposes a generalized definition and fitting function for time-dependent displacement distributions.

Findings

NGND can be a transient effect even at equilibrium.

Distributions may have sub-Gaussian tails, not just fat exponential tails.

A heuristic function can fit all time-dependent NGND distributions.

Abstract

Brownian particles suspended in disordered crowded environments often exhibit non-Gaussian normal diffusion (NGND), whereby their displacements grow with mean square proportional to the observation time and non-Gaussian statistics. Their distributions appear to decay almost exponentially according to "universal" laws largely insensitive to the observation time. This effect is generically attributed to slow environmental fluctuations, which perturb the local configuration of the suspension medium. To investigate the microscopic mechanisms responsible for the NGND phenomenon, we study Brownian diffusion in low dimensional systems, like the free diffusion of ellipsoidal and active particles, the diffusion of colloidal particles in fluctuating corrugated channels and Brownian motion in arrays of planar convective rolls. NGND appears to be a transient effect related to the time modulation of the instantaneous particle's diffusivity, which can occur even under equilibrium conditions. Consequently, we propose to generalize the definition of NGND to include transient displacement distributions which vary continuously with the observation time. To this purpose, we provide a heuristic one-parameter function, which fits all time-dependent transient displacement distributions corresponding to the same diffusion constant. Moreover, we reveal the existence of low dimensional systems where the NGND distributions are not leptokurtic (fat exponential tails), as often reported in the literature, but platykurtic (thin sub-Gaussian tails), i.e., with negative excess kurtosis. The actual nature of the NGND transients is related to the specific microscopic dynamics of the diffusing particle.