Anomalous Fourier's law and long range correlations in a 1D non-momentum conserving mechanical model

TL;DR

This study uses numerical simulations to show that a 1D mechanical heat transport model without momentum conservation exhibits anomalous Fourier's law and long-range correlations, challenging traditional theoretical expectations.

Contribution

It demonstrates that non-momentum conserving models can display anomalous heat conduction and correlations similar to momentum-conserving systems, contrary to Boltzmann equation predictions.

Findings

Model exhibits anomalous Fourier's law.

Presence of long-range correlations in velocity fields.

Contradicts Boltzmann equation predictions for this system.

Abstract

We study by means of numerical simulations the velocity reversal model, a one-dimensional mechanical model of heat transport introduced in 1985 by Ianiro and Lebowitz. Our numerical results indicate that this model, although it does not conserve momentum, exhibits an anomalous Fourier's law similar to the ones previously observed in momentum-conserving models. This is contrary to what is obtained from the solution of the Boltzmann equation (BE) for this system. The pair correlation velocity field also looks very different from the correlations usually seen in diffusive systems, and shares some similarity with those of momentum-conserving heat transport models.