Fourier law in the alternate mass hard-core potential chain

TL;DR

This paper investigates heat conduction in a one-dimensional chain of elastically colliding particles with alternating masses, demonstrating Fourier's law holds despite the absence of exponential dynamical instability, and highlights the importance of momentum conservation.

Contribution

It provides numerical evidence that Fourier law applies in a model with alternate masses and broken momentum conservation, contrasting with previous models.

Findings

Fourier law is valid in the studied model.

Momentum conservation influences heat transport behavior.

The model lacks exponential dynamical instability.

Abstract

We study energy transport in a one-dimensional model of elastically colliding particles with alternate masses $m$ and $M$. In order to prevent total momentum conservation we confine particles with mass $M$ inside a cell of finite size. We provide convincing numerical evidence for the validity of Fourier law of heat conduction in spite of the lack of exponential dynamical instability. Comparison with previous results on similar models shows the relevance of the role played by total momentum conservation.