The Lorentz Gas in a Mean-Field Potential: Weak Coupling and Diffusive Regime

TL;DR

This paper studies the Lorentz gas with a mean-field external force, showing that under weak coupling and diffusive timescales, the particle's distribution converges to a heat equation with a diffusion coefficient derived from the Green-Kubo relation.

Contribution

It demonstrates the diffusive limit of the Lorentz gas with mean-field forces and derives the diffusion coefficient via the Green-Kubo formula.

Findings

Convergence to the heat equation in the diffusive regime

Diffusion coefficient given by Green-Kubo relation

Validation of diffusive scaling in mean-field Lorentz gas

Abstract

We investigate the diffusive scaling of the Lorentz gas in the presence of an external force of mean-field type. In the weak coupling regime and for diffusive time scales, the test particle's law converges to the probability density satisfying the heat equation. The diffusion coefficient of the heat equation is given by the Green-Kubo relation.