Microcanonical quasi-stationarity of long-range interacting systems in contact with a heat bath

On the basis of analytical results and molecular dynamics simulations we clarify the nonequilibrium dynamics of a long-range interacting system in contact with a heat bath. For small couplings with the bath, we show that the system can first be trapped in a Vlasov quasi-stationary state, then a microcanonical one follows, and finally canonical equilibrium is reached at the bath temperature. We compare a Langevin mesoscopic thermostat with Hamiltonian reservoirs microscopically coupled with the system and demonstrate the equivalence of the two descriptions. Our identification of the parameters determining the quasi-stationary lifetimes could be exploited to control experimental systems such as the Free Electron Laser, in the presence of external noise or inherent imperfections.