Heating Rates under Fast Periodic Driving beyond Linear Response

Abstract

Heating under periodic driving is a generic nonequilibrium phenomenon, and it is a challenging problem in nonequilibrium statistical physics to derive a quantitatively accurate heating rate. In this work, we provide a simple formula on the heating rate under fast and strong periodic driving in classical and quantum many-body systems. The key idea behind the formula is constructing a time-dependent dressed Hamiltonian by moving to a rotating frame, which is found by a truncation of the high-frequency expansion of the micromotion operator, and applying the linear-response theory. It is confirmed for specific classical and quantum models that the second-order truncation of the high-frequency expansion yields quantitatively accurate heating rates beyond the linear-response regime. Our result implies that the information on heating dynamics is encoded in the first few terms of the high-frequency expansion, although heating is often associated with an asymptotically divergent behavior of the high-frequency expansion.

6+7 pages. To appear in Phys. Rev. Lett

References in corpus (3)

• Equilibrium states of generic quantum systems subject to periodic driving
• Coherent control of dressed matter waves
• Fermi's golden rule for heating in strongly driven Floquet systems

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• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems
• Stalled response near thermal equilibrium in periodically driven systems
• Quantum fingerprints of self-organization in spin chains coupled to a Kuramoto model
• Engineering micromotion in Floquet prethermalization via space-time symmetries