Heating Rates under Fast Periodic Driving beyond Linear Response

TL;DR

This paper derives a simple, accurate formula for the heating rate in classical and quantum many-body systems under fast periodic driving, extending beyond linear response by using a truncated high-frequency expansion.

Contribution

It introduces a method to calculate heating rates using a truncated high-frequency expansion and rotating frame transformation, providing quantitative accuracy beyond linear response.

Findings

Second-order truncation yields accurate heating rates

The method applies to both classical and quantum models

Heating information is contained in the first few high-frequency expansion terms

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.