Slow relaxation in long-range interacting systems with stochastic dynamics

TL;DR

This paper investigates how stochastic dynamics affect the long-lived quasistationary states in long-range interacting systems, showing that stochasticity causes these states to relax faster, eliminating their divergence with system size.

Contribution

It extends the Hamiltonian Mean-Field model to include stochastic processes and demonstrates that stochasticity removes the algebraic divergence of relaxation times.

Findings

Quasistationary states are only crossover phenomena under stochastic dynamics.

Relaxation times do not diverge algebraically with system size in the presence of stochasticity.

Stochastic processes lead to faster relaxation to equilibrium.

Abstract

Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which diverge algebraically with the system size. To test the robustness of this phenomenon to non-deterministic dynamical processes, we have generalized the paradigmatic model exhibiting such a behavior, the Hamiltonian Mean-Field model, to include energy-conserving stochastic processes. Analysis, based on the Boltzmann equation, a scaling approach and numerical studies, demonstrates that in the long time limit, the system relaxes to the equilibrium state on timescales which do not diverge algebraically with the system size. Thus, quasistationarity takes place only as a crossover phenomenon on times determined by the strength of the stochastic process.