A two-stage approach to relaxation in billiard systems of locally confined hard spheres

TL;DR

This paper investigates the macroscopic heat conduction in systems of confined hard spheres, showing that as interactions diminish, the system's behavior simplifies due to effective memory loss, with implications for diffusion in mixtures.

Contribution

It introduces a two-stage approach to analyze relaxation in confined billiard systems, linking microscopic dynamics to macroscopic heat conduction behavior.

Findings

Heat conduction coefficient reduces to a dimensional formula at low interaction rates.

System exhibits effective memory loss in the limit of vanishing interactions.

Similarities are drawn between this system and diffusion in binary mixtures.

Abstract

We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized.