Asymptotic Prethermalization in Periodically Driven Classical Spin Chains

TL;DR

This paper demonstrates a classical analog of quantum prethermalization in a chaotic spin chain, showing a long-lived prethermal state with a transition to infinite temperature, governed by drive frequency.

Contribution

It provides evidence that classical systems exhibit prethermalization similar to quantum systems, extending Floquet engineering concepts to classical many-body dynamics.

Findings

Prethermal plateau duration scales exponentially with drive frequency.

Transition from prethermal to thermal state is sharp and frequency-dependent.

Prethermal physics can be described by inverse-frequency expansion in classical systems.

Abstract

We reveal a continuous dynamical heating transition between a prethermal and an infinite-temperature stage in a clean, chaotic periodically driven classical spin chain. The transition time is a steep exponential function of the drive frequency, showing that the exponentially long-lived prethermal plateau, originally observed in quantum Floquet systems, survives the classical limit. Even though there is no straightforward generalization of Floquet's theorem to nonlinear systems, we present strong evidence that the prethermal physics is well described by the inverse-frequency expansion. We relate the stability and robustness of the prethermal plateau to drive-induced synchronization not captured by the expansion. Our results set the pathway to transfer the ideas of Floquet engineering to classical many-body systems, and are directly relevant for photonic crystals and cold atom experiments in the superfluid regime.