Abstract

Zoom link: https://maths-cam-ac-uk.zoom.us/j/94018037756

Quantum and classical systems can be driven into interesting and potentially useful non-equilibrium states by the application of time-periodic forcing. Phenomena such as time-crystallization and prethermalization can stabilize these non-equilibrium states against unwanted heating (absorption of energy) from the periodic drive. Prethermalization, in particular, occurs when a rapidly driven system relaxes quickly to an equilibrium-like “prethermal” state, in which it remains for a very long time – often exponential in the driving frequency – before ultimately absorbing energy from the drive. Insight into this phenomenon can be gained by studying the general problem of a classical, chaotic system under periodic driving at frequency ω≫1 (in appropriate units). I will argue that the system’s energy evolves diffusively, and I will present a Fokker-Planck equation for the statistical evolution of the system’s energy. This equation reveals that the system initially absorbs energy extremely slowly, at a rate that generically scales like e^(-ω), in agreement with prethermalization. For many-body systems, these results can be restated in terms of the system’s temperature, which remains at a near-constant value during the long prethermal era, before increasing indefinitely thereafter. Finally, I will combine semiclassical approximations with Fermi’s Golden Rule to argue that the same Fokker-Planck equation can be derived for rapidly driven quantum systems.