Noise-induced dynamical phase transitions in long-range systems

In the thermodynamic limit, the time evolution of isolated long-range interacting systems is properly described by the Vlasov equation. This equation admits non-equilibrium dynamically stable stationary solutions characterized by a zero order parameter. We show that the presence of external noise sources, like for instance a heat bath, can induce at a specific time a dynamical phase transition marked by a non-zero order parameter. This transition corresponds to a restoring of the full ergodic properties of the system and may be used as a distinctive experimental signature of the existence of non-equilibrium Vlasov-stable states. In particular, we evidence for the first time a regime characterized by an order parameter pulse. Our analytical results are corroborated by numerical simulations of a paradigmatic long-range model.