Diffusion with restrictions

TL;DR

This paper derives a nonlinear diffusion model considering occupation-dependent hopping rates, revealing anomalous diffusion behavior with a time-dependent bump and discussing its relevance to glassy systems.

Contribution

It introduces a novel nonlinear diffusion equation incorporating occupation-dependent hopping, leading to new insights into anomalous diffusion and its fractal properties.

Findings

Presence of a time-dependent bump in diffusion profile

Anomalous diffusion exponent characterizing the bump's movement

Fractal dimension depends solely on space dimension

Abstract

A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The stationary and the time dependent behaviour of the system are studied based upon the master equation approach. Different to conventional diffusion it results a time dependent bump the position of which increases with time described by an anomalous diffusion exponent. The fractal dimension of this random walk is exclusively determined by the space dimension. The applicabilty of the model to descibe glasses is discussed.