Noise-induced dynamical phase transitions in long-range systems

TL;DR

This paper demonstrates that external noise can induce dynamical phase transitions in long-range systems, restoring ergodicity and revealing non-equilibrium Vlasov-stable states through observable order parameter pulses.

Contribution

It introduces the concept that noise can trigger phase transitions in long-range systems, providing analytical and numerical evidence for this phenomenon.

Findings

External noise induces dynamical phase transitions.

Restoration of ergodic properties in long-range systems.

Observation of order parameter pulses as signatures.

Abstract

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.