Reservoir-induced stabilisation of a periodically driven classical spin chain: local vs. global relaxation

TL;DR

This paper investigates how a classical spin chain driven periodically and coupled to a thermal reservoir exhibits different relaxation behaviors, highlighting the roles of frequency, reservoir dynamics, and synchronization.

Contribution

It expands previous work by analyzing higher-order Floquet-Magnus corrections, reservoir evolution, and synchronization in classical driven spin chains.

Findings

High-frequency regime shows local Floquet-Gibbs ensemble with near-reversible heat sink behavior.

Low-frequency regime leads to rapid global synchronization involving reservoir relaxation.

Reservoir evolution can be incorporated via an effective temperature in a local picture.

Abstract

Floquet theory is an indispensable tool for analysing periodically-driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviours of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution the dynamics of the reservoir; and further explore how the driven system synchronises with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterised by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heatsink. At low frequencies, the driven system rapidly enters a synchronised state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we argue that dissipative equations of motion for periodically-driven many-body systems, at least at intermediate frequencies, must generically be non-Markovian.