Energy diffusion in hard-point systems

TL;DR

This paper studies energy diffusion in a one-dimensional diatomic hard-point chain, revealing a universal Levy walk behavior with specific anomalies at zero pressure and effects of internal degrees of freedom.

Contribution

It demonstrates the universality class of energy diffusion in the model and explores the effects of zero-pressure conditions and internal degrees of freedom on diffusion behavior.

Findings

Energy fluctuations follow a Levy walk with exponent 3/5.

Zero-pressure limit shows normal diffusion in tangent space but anomalous for finite perturbations.

Internal degrees of freedom do not alter the overall diffusion scenario.

Abstract

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the "stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenario