Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving

In this talk, I will discuss energy absorption for a chaotic billiard particle subject to a rapid, periodic driving force, with driving frequency ω. The energy dynamics of this particle can be described as a process of diffusion in energy space, wherein the particle's energy probability distribution shifts and spreads according to a Fokker-Planck equation. This model has several interesting features, including a statistical bias towards energy growth, and an energy absorption rate which is suppressed by a factor of 1/ω². I will briefly summarize the derivation of this model, and then present explicit expressions for the associated rates of energy absorption and diffusion. I will also present numerical simulations which corroborate the energy diffusion description. Finally, I will frame these results as a case study of the phenomenon of prethermalization, and argue that the billiard model may offer insight into certain prethermal many-body interacting systems, both classical and quantum.