Heat conduction and diffusion of hard disks in a narrow channel

TL;DR

This study uses molecular dynamics to analyze heat conduction and diffusion of hard disks in narrow channels, revealing divergence in heat conductivity with system size under momentum-conserving collisions and finite conductivity otherwise.

Contribution

It demonstrates how momentum conservation influences heat conduction scaling and diffusion behavior in one-dimensional hard disk systems.

Findings

Heat conductivity diverges as N^1/3 with momentum conservation.

Normal diffusion occurs on an intermediate time scale due to sound waves.

Non-momentum conserving collisions result in finite heat conductivity.

Abstract

Using molecular dynamics we study heat conduction and diffusion of hard disks in one dimensional narrow channels. When collisions preserve momentum the heat conduction $\kappa$ diverges with the number of disks $N$ as $\kappa\sim N^\alpha$ $(\alpha \approx 1/3)$. Such a behaviour is seen both when the ordering of disks is fixed ('pen-case' model), and when they can exchange their positions. Momentum conservation results also in sound-wave effects that enhance diffusive behaviour and on an intermediate time scale (that diverges in the thermodynamic limit) normal diffusion takes place even in the 'pen-case' model. When collisions do not preserve momentum, $\kappa$ remains finite and sound-wave effects are absent.