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When a chaotic, ergodic Hamiltonian system with $N$ degrees of freedom issubject to sufficiently rapid periodic driving, its energy evolves diffusively.We derive a Fokker-Planck equation that governs the evolution of the system'sprobability distribution in energy space, and we provide explicit expressionsfor the energy drift and diffusion rates. Our analysis suggests that the systemgenerically relaxes to a long-lived "prethermal" state characterized by minimalenergy absorption, eventually followed by more rapid heating. When $N\gg 1$,the system ultimately absorbs energy indefinitely from the drive, or at leastuntil an infinite temperature state is reached.

Energy diffusion and absorption in chaotic systems with rapid periodic driving