Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model

TL;DR

This paper investigates the unusual N^1.7 scaling law of quasistationary state lifetimes in the Hamiltonian Mean-Field model, revealing the role of local dynamics and diffusion in explaining this behavior.

Contribution

It introduces a mean first passage time approach to explain the non-trivial scaling of QSS lifetimes in long-range interacting systems.

Findings

The N^1.7 scaling law arises from local dynamics and diffusion properties.

The mean first passage time approach successfully explains the observed scaling.

Insights are provided into cases with exponentially diverging lifetimes above critical energy.

Abstract

Out-of-equilibrium quasistationary states (QSSs) are one of the signatures of a broken ergodicity in long-range interacting systems. For the widely studied Hamiltonian Mean-Field model, the lifetime of some QSSs has been shown to diverge with the number N of degrees of freedom with a puzzling N^1.7 scaling law, contradicting the otherwise widespread N scaling law. It is shown here that this peculiar scaling arises from the locality properties of the dynamics captured through the computation of the diffusion coefficient in terms of the action variable. The use of a mean first passage time approach proves to be successful in explaining the non-trivial scaling at stake here, and sheds some light on another case, where lifetimes diverging as e^N above some critical energy have been reported.