Prethermalization and conservation laws in quasi-periodically-driven quantum systems

TL;DR

This paper investigates how quasi-periodic driving influences conservation laws in quantum many-body systems, demonstrating long-lived prethermal states and quasi-conservation of certain quantities under specific conditions.

Contribution

It provides a rigorous proof of Nekhoroshev-type stability and quasi-conservation laws in driven quantum systems, extending understanding of their long-term behavior.

Findings

Prethermal states last exponentially long under certain driving conditions

Constants of motion are approximately conserved in driven systems

Analysis applies to models relevant in condensed matter physics

Abstract

We study conservation laws of a general class of quantum many-body systems subjected to an external time dependent quasi-periodic driving. {When the frequency of the driving is large enough or the strength of the driving is small enough, we prove a Nekhoroshev-type stability result: we show that the system exhibits a prethermal state for stretched exponentially long times in the perturbative parameter}. Moreover, we prove the quasi-conservation of the constants of motion of the unperturbed Hamiltonian and we analyze their physical meaning in examples of relevance to condensed matter and statistical physics.