A universal model for Floquet prethermalization in classical chaotic systems.

  Sadia Yonathan  ,  Emanuele G Dalla Torre  ,  Atanu Rajak  
Department of Physics and Center for Quantum Entanglement in Science and Technology, Bar-Ilan University, Israel

When chaotic systems are driven by fast periodic drives, they often absorb energy at exponentially low rates. This phenomenon, known as Floquet prethermalization, obeys rigorous bounds only in quantum systems with small local Hilbert spaces. In systems with unbounded spectra, Floquet prethermalization can nevertheless emerge from statistical arguments, predicting an exponential dependence of the heating rate on the ratio between the  driving frequency  and the initial temperature. Here, we demonstrate the universality of this effect by studying the roles of initial conditions and connectivity. We demonstrate that both effects are captured by a simple statistical description, based on the time-dependence of a single quasi-conserved quantity, namely the average energy. The resulting differential equation can be solved analytically and offers an accurate description of our numerical observations.