Conditions for quantum violent relaxation

While the dynamics of fully connected systems is dominated by mean-field effect, in the classical limit the single-particle observables are observed to relax toward a nonthermal stationary value. This phenomenon is known as violent relaxation and it is generally absent at the quantum-mechanical level, where single-particle observables exhibits long-lived oscillations. In this paper we explain this discrepancy by determining some very restrictive conditions that quantum single-site Hamiltonians should meet in order for the system to undergo relaxation. We thus check them by introducing a new model (the so-called $w$ model) which can exhibit dynamical phase transition among thermal behavior, persistent excitations, and violent relaxation. We also propose a way to implement it within light-matter coupling. We finally explain how the classical limit restore this behavior, thus showing that, even if the mean-field dynamics of quantum models is usually thought to be classical, quantum effects still play an important role in it.