One dimensional heat conductivity exponent from random collision model

TL;DR

This paper numerically investigates the heat conductivity scaling in quasi-one-dimensional models, confirming the theoretical exponent of 1/3 in a highly chaotic, energy- and momentum-conserving system.

Contribution

It introduces a new ergodic, chaotic model that accurately captures heat conduction scaling at small system sizes, aligning with theoretical predictions.

Findings

Thermal conductivity scales as L^{1/3} over two decades.

The new model is ergodic, chaotic, and conserves energy and momentum.

Results confirm the analytical prediction of the heat conductivity exponent.

Abstract

We study numerically the thermal conductivity coefficient $\kappa$ as a function of system length $L$ for several different quasi one dimensional models: classical gases of hard spheres with both longitudinal and transverse degrees of freedom. We introduce a model that is ergodic and highly chaotic but also conserves energy and momentum, and is very useful because it shows scaling even at small system sizes. We find that $\kappa \sim L^\alpha$ over more than two decades, with $\alpha$ very close to the analytical prediction of 1/3.