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

5+6 pages, 3 figures; typos corrected

References in corpus (22)

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• Coherent destruction of tunneling, dynamic localization and the Landau-Zener formula
• Stroboscopic prethermalization in weakly interacting periodically driven systems
• Non-equilibrium phase transition in a periodically driven XY spin chain
• Floquet resonant states and validity of the Floquet-Magnus expansion in the periodically driven Friedrichs models

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