Relaxation dynamics of stochastic long-range interacting systems

Abstract

Long-range interacting systems, while relaxing towards equilibrium, may get trapped in nonequilibrium quasistationary states (QSS) for a time which diverges algebraically with the system size. These intriguing non-Boltzmann states have been observed under deterministic Hamiltonian evolution of a paradigmatic system, the Hamiltonian Mean-Field (HMF) model. We study here the robustness of QSS with respect to stochastic processes beyond deterministic dynamics within a microcanonical ensemble. To this end, we generalize the HMF model by allowing for stochastic three-particle collision dynamics in addition to the deterministic ones. By analyzing the resulting Boltzmann equation for the phase space density, we demonstrate that in the presence of stochasticity, QSS occur only as a crossover phenomenon over a finite time determined by the strength of the stochastic process. In particular, we argue that the relaxation time to equilibrium does not scale algebraically with the system size. We propose a scaling form for the relaxation time which is in very good agreement with results of extensive numerical simulations. The broader validity of these results is tested on a different stochastic HMF model involving microcanonical Monte Carlo dynamical moves.

23 pages, 6 figures. v2: minor changes with added references, published version

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• Scaling quasi-stationary states in long range systems with dissipation
• Slow dynamics of interacting antiferromagnetic nanoparticles
• Attractor non-equilibrium stationary states in perturbed long-range interacting systems
• Sampling microcanonical measures of the 2D Euler equations through Creutz's algorithm: a phase transition from disorder to order when energy is increased
• Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces