Dynamical phase transitions in long-range Hamiltonian systems and Tsallis distributions with a time-dependent index.

摘要: We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian mean field model as a simple example. These generically undergo violent relaxation to quasistationary state (QSS) before relaxing towards Boltzmann equilibrium. In collisional regime, out-of-equilibrium one-particle distribution function (DF) is solution of Vlasov equation, slowly evolving time due finite-$N$ effects. For subcritical energy densities, we exhibit cases where DF well fitted by Tsallis $q$ an index $q(t)$ decreasing from $q\ensuremath{\simeq}3$ (semiellipse) $q=1$ (Boltzmann). When reaches energy-dependent critical value ${q}_{\mathit{crit}}$, nonmagnetized (homogeneous) becomes unstable and transition triggered, leading magnetized (inhomogeneous) state. While distributions play important role our study, explain this only conventional statistical mechanics. supercritical report existence QSS very long lifetime.