Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving

TL;DR

This paper investigates how a particle in a chaotic billiard under rapid periodic driving exhibits diffusive energy growth, characterized by a Fokker-Planck equation, revealing phases of prethermalization, slow absorption, and eventual breakdown at high energies.

Contribution

The study provides a theoretical and numerical analysis of energy diffusion in chaotic billiards under high-frequency driving, introducing a Fokker-Planck framework and identifying distinct energy evolution phases.

Findings

Energy absorption rates scale as ω^{-2} at high frequencies.

Energy distribution follows a Fokker-Planck equation in the diffusive regime.

Numerical simulations support the theoretical energy evolution phases.

Abstract

We study the energy dynamics of a particle in a billiard subject to a rapid periodic drive. In the regime of large driving frequencies $\omega$, we find that the particle's energy evolves diffusively, which suggests that the particle's energy distribution $\eta (E,t)$ satisfies a Fokker-Planck equation. We calculate the rates of energy absorption and diffusion associated with this equation, finding that these rates are proportional to $\omega^{-2}$ for large $\omega$. Our analysis suggests three phases of energy evolution: Prethermalization on short timescales, then slow energy absorption in accordance with the Fokker-Planck equation, and finally a breakdown of the rapid driving assumption for large energies and high particle speeds. We also present numerical simulations of the evolution of a rapidly driven billiard particle, which corroborate our theoretical results.