Convergence to a Gaussian by narrowing of central peak in Brownian yet non-Gaussian diffusion in disordered environments

TL;DR

This paper explores how diffusion in strongly disordered environments can deviate from typical Gaussian convergence, maintaining sharp features over time, which has implications for diagnosing disorder in complex systems.

Contribution

It demonstrates that in disordered media with infinite contrast, the usual smoothing to a Gaussian does not occur, revealing a novel aspect of diffusion behavior.

Findings

Sharp features persist at long times in strong disorder

Diffusion can be non-Gaussian despite long-time limits

Implications for diagnosing disorder in biological systems

Abstract

In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g. biological, systems.