Entropy maximizers for kinetic wave equations set on tori

TL;DR

This paper studies the kinetic wave equation on tori, characterizing entropy maximizers across dimensions and dispersion relations, including quantum cases, and analyzing conditions for wave condensation.

Contribution

It provides a general framework for entropy maximizers of the kinetic wave equation, encompassing quantum cases and identifying regimes with wave condensation.

Findings

Entropy maximizers characterized for various dimensions and dispersion relations.

Condensation phenomena identified and described in specific regimes.

Framework applicable to quantum kinetic wave equations.

Abstract

We consider the kinetic wave equation, or phonon Boltzmann equation, set on the torus (physical system set on the lattice). We describe entropy maximizers for fixed mass and energy; our framework is very general, being valid in any dimension, for any dispersion relation, and even including the quantum kinetic wave equation. Of particular interest is the presence of condensation in certain regimes which we characterize.