Diffusivity of lattice gases

TL;DR

This paper investigates the diffusivity properties of one-component lattice gases with local dynamics, providing bounds and confirming diffusive or superdiffusive behavior based on the model's characteristics.

Contribution

It offers rigorous bounds on diffusivity and establishes conditions under which the lattice gas exhibits diffusive or superdiffusive behavior.

Findings

Bounds on diffusivity depending on dimension and flux function

Confirmation of diffusive behavior when expected

Confirmation of superdiffusive behavior when expected

Abstract

We consider one component lattice gases with a local dynamics and a stationary product Bernoulli measure. We give upper and lower bounds on the diffusivity at an equilibrium point depending on the dimension and the local behavior of the macroscopic flux function. We show that if the model is expected to be diffusive, it is indeed diffusive, and, if it is expected to be superdiffusive, it is indeed superdiffusive.