Reservoir-induced stabilization of a periodically driven many-body system

Exploiting the rich phenomenology of periodically driven many-body systems is notoriously hindered by persistent heating in both the classical and the quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilization of a nontrivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and we simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite frequency and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a global synchronized Gibbs state emerges, whose temperature may depart significantly from the initial temperature of the reservoir. Although our analysis in some parts relies on the specific properties of our setup, we argue that much of its phenomenology could be generic.

Automated summary

This article investigates the stability of steady states in many-body systems coupled to a large thermal reservoir. By modeling the system and the reservoir as classical spin chains and simulating the Hamiltonian dynamics, the authors find that at high frequencies, the system reaches a Floquet-type Gibbs state at the reservoir temperature, while at low frequencies, a global synchronized Gibbs state emerges with a potentially different temperature from the reservoir. The authors argue that although their analysis relies on specific properties of their setup, much of the phenomenology could be applicable to other systems.