Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems

TL;DR

This paper establishes that in strongly driven quantum systems, energy absorption is limited over long times, and an effective Hamiltonian governs the early relaxation, revealing universal relaxation behaviors.

Contribution

It provides a rigorous Floquet analysis demonstrating energy conservation and quasi-conservation of an effective Hamiltonian in periodically driven quantum systems.

Findings

Energy remains nearly constant up to exponentially long times in frequency.

Effective Hamiltonian acts as a quasi-conserved quantity during relaxation.

Initial relaxation resembles prethermalization in quasi-integrable systems.

Abstract

We discuss the universal nature of relaxation in isolated many-body quantum systems subjected to global and strong periodic driving. Our rigorous Floquet analysis shows that the energy of the system remains almost constant up to an exponentially long time in frequency for arbitrary initial states and that an effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion is a quasi-conserved quantity for long time scale. These two general properties lead to intriguing classification on the initial stage of relaxation, one of which is similar to the prethermalization phenomenon in quasi-integrable systems.