Well-posedness of the Cauchy problem for a space-dependent anyon Boltzmann equation

TL;DR

This paper establishes the global existence, uniqueness, and stability of strong solutions for a non-linear Boltzmann equation modeling anyons in a one-dimensional periodic setting, advancing the mathematical understanding of quantum statistical mechanics.

Contribution

It proves well-posedness for the space-dependent anyon Boltzmann equation with large initial data, a significant extension beyond previous results for quantum gases.

Findings

Global existence of solutions

Uniqueness of solutions

Stability under initial data variations

Abstract

A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and stability.