Out-of-Equilibrium Statistical Mechanics in a Hamiltonian System with Mean-Field Interaction

Abstract

Systems with finite degrees of freedom and with long-range interaction are frequently trapped at quasi-stationary states before relaxing to thermal equilibrium. Short-time relaxation to quasi-stationary states is approximated by the Vlasov equation, and a statistical theory based on the Vlasov description is introduced and applied to the Hamiltonian mean-field model. The theory predicts a one-body distribution for a quasi-stationary state from a given waterbag initial distribution, and a critical curve is described on a two-dimensional parameter plane which represents a family of waterbag initial distributions. The critical curve divides the parameter plane into magnetized and non-magnetized phases of quasi-stationary states. The theoretical prediction is checked by comparing with a numerically obtained critical curve for systems with finite degrees of freedom.