The Lorentz Process with a Nearly Periodic Distribution of Scatterers

TL;DR

This paper proves that a Lorentz gas with scatterers nearly periodic in distribution converges to a linear Boltzmann equation in the low density limit, unlike the purely periodic case.

Contribution

It establishes the Boltzmann limit for Lorentz gases with nearly periodic scatterer distributions, bridging the gap between random and periodic configurations.

Findings

Lorentz gas with nearly periodic scatterers converges to linear Boltzmann equation

Periodic Lorentz gas does not satisfy Boltzmann limit in the same way

Results clarify the impact of scatterer distribution on kinetic limits

Abstract

We consider the Lorentz gas in a distribution of scatterers which microscopically converges to a periodic distribution, and prove that the Lorentz gas in the low density limit satisfies a linear Boltzmann equation. This is in contrast with the periodic Lorentz gas, which does not satisfy the Boltzmann equation in the limit.