Dynamical quasi-stationary states in a system with long-range forces

The Hamiltonian Mean Field (HMF) model describes a system of N fully coupled particles showing a second-order phase transition as a function of the energy. The dynamics of the model presents interesting features in a small energy region below the critical point. In particular, when the particles are prepared in a “water bag” initial state, the relaxation to equilibrium is very slow. In the transient time the system lives in a dynamical quasi-stationary state and exhibits anomalous (enhanced) diffusion and Lévy walks. In this paper we study temperature and velocity distribution of the quasi-stationary state and we show that the lifetime of such a state increases with N. In particular when the N→∞ limit is taken before the t→∞ limit, the results obtained are different from the expected canonical predictions. This scenario seems to confirm a recent conjecture proposed by Tsallis [C. Tsallis, in: S.R.A. Salinas, C. Tsallis (Eds.), Nonextensive statistical mechanics and thermodynamics, Braz. J. Phys. 29 (1999) 1 cond-mat/9903356 and contribution to this conference.