Heat conductivity from molecular chaos hypothesis in locally confined billiard systems

TL;DR

This paper derives a Boltzmann-like equation to analyze heat transport in large, locally confined billiard systems with elastic collisions, and validates the theoretical predictions through numerical simulations.

Contribution

It introduces a novel approach to compute heat conductivity in Hamiltonian billiard systems using a Boltzmann-like equation derived from molecular chaos.

Findings

Derived a Boltzmann-like equation for the system

Computed heat conductivity using Green-Kubo formula

Validated predictions with numerical simulations

Abstract

We study the transport properties of a large class of locally confined Hamiltonian systems, in which neighboring particles interact through hard core elastic collisions. When these collisions become rare and the systems large, we derive a Boltzmann-like equation for the evolution of the probability densities. We solve this equation in the linear regime and compute the heat conductivity from a Green-Kubo formula. The validity of our approach is demonstated by comparing our predictions to the results of numerical simulations performed on a new class of high-dimensional defocusing chaotic billiards.