Prethermalization in aperiodically kicked many-body dynamics

TL;DR

This paper explores how aperiodic driving protocols like quasi-periodic and random sequences can suppress heating in many-body systems, leading to long-lived prethermal states with lifetimes depending on the drive's temporal correlations.

Contribution

It introduces a method to eliminate multiple heating channels in aperiodically driven systems, extending prethermalization concepts beyond high-frequency regimes.

Findings

Multiple heating channels can be suppressed in aperiodic drives.

Prethermal lifetime scales as a power law with drive strength, depending on multipolar order.

Long-lived prethermal regimes are observed in a classical kicked rotor chain.

Abstract

Driven many-body systems typically experience heating due to the lack of energy conservation. Heating may be suppressed for time-periodic drives, but little is known for less regular drive protocols. In this work, we investigate the heating dynamics in aperiodically kicked systems, specifically those driven by quasi-periodic Thue-Morse or a family of random sequences with $n$-multipolar temporal correlations. We demonstrate that multiple heating channels can be eliminated even away from the high-frequency regime. The number of eliminated channels increases with multipolar order $n$. We illustrate this in a classical kicked rotor chain where we find a long-lived prethermal regime. When the static Hamiltonian only involves the kinetic energy, the prethermal lifetime $t^*$ can strongly depend on the temporal correlations of the drive, with a power-law dependence on the kick strength $t^*\sim K^{-2n}$, for which we can account using a simple linearization argument.