Ergodicity breaking and quasistationary states in systems with long-range interactions.

In the thermodynamic limit, systems with long-range interactions do not relax to equilibrium, but become trapped in quasistationary states (qSS), the life time of which diverges with the number of particles. In this paper we will explore the relaxation of the Hamiltonian Mean-Field model to qSS for a class of initial conditions of the multilevel water-bag form. We will show that if the initial distribution satisfies the virial condition, thereby reducing mean field changes, the final distribution in the qSS can be predicted very accurately using a reduced exactly integrable model. The calculated distribution functions obtained using this approach are found to be more accurate than the ones predicted by the Lynden-Bell theory.