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

TL;DR

This study explores how coupling a periodically-driven classical spin system to a thermal reservoir can stabilize non-trivial steady states, revealing regimes where the system attains Gibbs states at the reservoir temperature or synchronizes with it.

Contribution

It demonstrates that reservoir coupling can stabilize steady states in driven many-body systems across a wide frequency range, extending known limits and revealing new dynamical regimes.

Findings

High-frequency driving leads to Floquet-Gibbs states at reservoir temperature.

Low-frequency driving results in synchronized Gibbs states with variable temperature.

The phenomenology is likely generic for a broad class of driven many-body systems.

Abstract

Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilisation of a non-trivial 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 simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite 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 synchronised Gibbs state emerges, whose temperature may depart significantly from that of the reservoir. Although our analysis in some parts relies on the specific properties our setup, we argue that much of its phenomenology should be generic for a large class of systems.