From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems

TL;DR

This paper demonstrates that energy diffusion in a one-dimensional diatomic gas exhibits Levy walk behavior, confirming anomalous heat conductivity with a divergence rate of approximately 1/3, aligning with theoretical predictions.

Contribution

It extends Levy walk descriptions to many-body systems and provides strong evidence for anomalous energy diffusion and heat conductivity divergence in the HPG model.

Findings

Energy diffusion is anomalous in the HPG.

Heat conductivity diverges with an exponent of about 1/3.

Levy walk description applies to many-body systems.

Abstract

The evolution of infinitesimal, localized perturbations is investigated in a one-dimensional diatomic gas of hard-point particles (HPG) and thereby connected to energy diffusion. As a result, a Levy walk description, which was so far invoked to explain anomalous heat conductivity in the context of non-interacting particles is here shown to extend to the general case of truly many-body systems. Our approach does not only provide a firm evidence that energy diffusion is anomalous in the HPG, but proves definitely superior to direct methods for estimating the divergence rate of heat conductivity which turns out to be $0.333\pm 0.004$, in perfect agreement with the dynamical renormalization--group prediction (1/3).