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

Heating Rates under Fast Periodic Driving beyond Linear Response