Low-energy prethermal phase and crossover to thermalization in nonlinear kicked rotors

TL;DR

This paper investigates the dynamical phases of nonlinear kicked rotors with interactions, revealing a low-energy prethermal phase with light-cone correlation spreading and a complex transition to thermalization.

Contribution

It introduces a hydrodynamic theory for the prethermal phase and maps out the rich dynamical phase diagram, including sharp crossovers to thermalization.

Findings

Identification of a low-energy prethermal phase with light-cone correlation spreading

Development of a hydrodynamic theory matching numerical simulations

Mapping of the dynamical phase diagram and thermalization crossovers

Abstract

In the presence of interactions, periodically-driven quantum systems generically thermalize to an infinite-temperature state. Recently, however, it was shown that in random kicked rotors with local interactions, this long-time equilibrium could be strongly delayed by operating in a regime of weakly fluctuating random phases, leading to the emergence of a metastable thermal ensemble. Here we show that when the random kinetic energy is smaller than the interaction energy, this system in fact exhibits a much richer dynamical phase diagram, which includes a low-energy pre-thermal phase characterized by a light-cone spreading of correlations in momentum space. We develop a hydrodynamic theory of this phase and find a very good agreement with exact numerical simulations. We finally explore the full dynamical phase diagram of the system and find that the transition toward full thermalization is characterized by relatively sharp crossovers.