Discrete Boltzmann Equation for Anyons

TL;DR

This paper develops and analyzes a discretized Boltzmann equation model for anyons, fractional-statistics particles, studying their equilibrium behavior and linearized operator properties in planar and homogeneous systems.

Contribution

It introduces a semi-classical, discretized Boltzmann equation framework for anyons, extending kinetic theory to fractional statistics particles.

Findings

Proves properties of the linearized operator for the discrete Boltzmann equation.

Analyzes trend to equilibrium in planar and homogeneous systems.

Establishes applicability of steady half-space problem results to the discrete model.

Abstract

A semi-classical approach to the study of the evolution of anyonic excitations--elementary particles with fractional statistics, complementing bosons and fermions--is through the Boltzmann equation for anyons. This work reviews a discretized version--a system of partial differential equations--of such a quantum equation. Trend to equilibrium is studied for a planar stationary system, as well as the spatially homogeneous system. Essential properties of the linearized operator are proven, implying that results for general steady half-space problems for the discrete Boltzmann equation in a slab geometry can be applied.