Mass fluctuations and diffusion in time-dependent random environments

TL;DR

This paper investigates how particles diffuse and form fluctuating mass densities in time-dependent random environments, revealing universal power-law tails and scale-dependent spatial properties.

Contribution

It introduces a mass ejection model in dynamic environments, analyzing diffusion, stationary states, and the statistical properties of mass density fluctuations.

Findings

Particles diffuse with Gaussian displacement distribution at large times.

Mass density exhibits large fluctuations with power-law tails.

The right tail exponent is universally -3/2 for differentiable environments.

Abstract

A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large times with a displacement distribution that approaches a Gaussian. The collective dynamics of diffusing particles reaches a statistically stationary state, which is characterized in terms of a fluctuating mass density field. The probability distribution of density is studied numerically for both smooth and non-smooth scale-invariant random environments. A competition between trapping in the regions where the ejection rate of the environment vanishes and mixing due to its temporal dependence leads to large fluctuations of mass. These mechanisms are found to result in the presence of intermediate power-law tails in the probability distribution of the mass density. For spatially differentiable environments, the exponent of the right tail is shown to be universal and equal to -3/2. However, at small values, it is found to depend on the environment. Finally, spatial scaling properties of the mass distribution are investigated. The distribution of the coarse-grained density is shown to posses some rescaling properties that depend on the scale, the amplitude of the ejection rate, and the H\"older exponent of the environment.