Energy diffusion and prethermalization in chaotic billiards under rapid periodic driving

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.

15 pages, 5 figures

References in corpus (4)

• Equilibrium states of generic quantum systems subject to periodic driving
• Periodically driven ergodic and many-body localized quantum systems
• Hyperacceleration in a stochastic Fermi-Ulam model
• Exponential Fermi acceleration in general time-dependent billiards

Cited by in corpus (3)

• Sharp detection of the onset of Floquet heating using eigenstate sensitivity
• Energy-space random walk in a driven disordered Bose gas
• Oscillating states of driven Langevin systems in large viscous regime