Study on non-equilibrium quasi-stationary states for Hamiltonian systems with long-range interaction

Joyce, Michael, Jules Morand, Pascal Viot

Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle number. We show here that, by applying a suitable perturbation operator for a finite time interval, we obtain, in a family of long-range systems, non-equilibrium states which appear to be strictly stationary. They exist even in the case of a harmonic potential, and are characterised by an ordered microscopic phase space structure. We give some simple heuristic arguments which predict reasonably well some properties of these states.

Yoshiyuki Y. Yamaguchi

Vasily Evgenevich Tarasov

Fulvio Baldovin, Enzo Orlandini

We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the Hamiltonian Mean Field model and the equilibrium ensemble equivalence. We find that long-lasting quasi-stationary states persist in presence of the interaction with the environment. Our results indicate that quasi-stationary states are indeed reproducible in real physical experiments.

Antonio Rodríguez, Fernando Dantas Nobre, Constantino Tsallis

This paper studies the duration of quasi-stationary states, typical of long-range-interacting Hamiltonians where negative specific heat emerges. For the classical Heisenberg d-dimensional model, the authors show a universal behavior on the time evolution of the average kinetic energy per particle as a function of dimension, system size, and range of the interactions.

Duccio Fanelli