  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.
