Metastability results for a class of linear Boltzmann equations

TL;DR

This paper analyzes a semiclassical linear Boltzmann model with non-local collisions, providing spectral asymptotics, metastability results, and insights into the rate of return to equilibrium using advanced mathematical techniques.

Contribution

It introduces sharp spectral asymptotics and metastability results for a class of linear Boltzmann equations in the low temperature regime.

Findings

Spectral asymptotics for the small spectrum at low temperatures

Quantitative rate of return to equilibrium

Metastability behavior in the model

Abstract

We consider a semiclassical linear Boltzmann model with a non local collision operator. We provide sharp spectral asymptotics for the small spectrum in the low temperature regime from which we deduce the rate of return to equilibrium as well as a metastability result. The main ingredients are resolvent estimates obtained via hypocoercive techniques and the construction of sharp Gaussian quasimodes through an adaptation of the WKB method.