Energy Transfer and Joint Diffusion

TL;DR

This paper proposes a model for the diffusive behavior of two interacting Lorentz disks in a periodic environment, showing their joint trajectories converge to a mixture of Gaussian laws, with implications for understanding particle diffusion.

Contribution

It introduces a new paradigm model for the diffusive limit of two Lorentz disks with elastic collisions, extending understanding of joint diffusion behavior.

Findings

Joint trajectories converge to a mixture of Gaussian laws.

The model predicts similar behavior for the mechanical Lorentz disk system.

Provides a framework for analyzing diffusive limits in interacting particle systems.

Abstract

A paradigm model is suggested for describing the diffusive limit of trajectories of two Lorentz disks moving in a finite horizon periodic configuration of smooth, strictly convex scatterers and interacting with each other via elastic collisions. For this model the diffusive limit of the two trajectories is a mixture of joint Gaussian laws (analogous behavior is expected for the mechanical model of two Lorentz disks).