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

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.

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• Generalization of the possible algebraic basis of $q$-triplets
• Quasistationarity in a long-range interacting model of particles moving on a sphere
• Caloric curves fitted by polytropic distributions in the HMF model
• Crafting networks to achieve, or not achieve, chaotic states
• Mass Segregation Phenomena using the Hamiltonian Mean Field Model