Slow Relaxation in LongRange Interacting Systems with Stochastic Dynamics
Abstract
Quasistationary states are longlived nonequilibrium states, observed in some systems with longrange interactions under deterministic Hamiltonian evolution. These intriguing nonBoltzmann states relax to equilibrium over times which diverge algebraically with the system size. To test the robustness of this phenomenon to nondeterministic dynamical processes, we have generalized the paradigmatic model exhibiting such a behavior, the Hamiltonian meanfield model, to include energyconserving 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 time scales 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.
 Publication:

Physical Review Letters
 Pub Date:
 July 2010
 DOI:
 10.1103/PhysRevLett.105.040602
 arXiv:
 arXiv:1006.0233
 Bibcode:
 2010PhRvL.105d0602G
 Keywords:

 05.20.y;
 05.40.a;
 05.70.Ln;
 Classical statistical mechanics;
 Fluctuation phenomena random processes noise and Brownian motion;
 Nonequilibrium and irreversible thermodynamics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 4+ pages, 1 figure