Diffusive limit for the random Lorentz gas

TL;DR

This paper reviews recent progress in deriving the diffusion equation and validating Fick's law from the microscopic random Lorentz gas model, using a linear kinetic equation as an intermediate step.

Contribution

It introduces a framework connecting the microscopic Lorentz gas to macroscopic diffusion through a linear kinetic equation, providing rigorous derivations and validations.

Findings

Derivation of the diffusion equation from the Lorentz gas

Validation of Fick's law in the microscopic model

Use of linear kinetic equation as an intermediate description

Abstract

We review some recent results concerning the derivation of the diffusion equation and the validation of Fick's law for the microscopic model given by the random Lorentz Gas. These results are achieved by using a linear kinetic equation as an intermediate level of description between our original mechanical system and the diffusion equation.