Energy diffusion and absorption in chaotic systems with rapid periodic driving

TL;DR

This paper derives a Fokker-Planck equation describing energy diffusion in chaotic Hamiltonian systems under rapid periodic driving, revealing a prethermal state and eventual heating, especially prominent in systems with many degrees of freedom.

Contribution

It provides explicit formulas for energy drift and diffusion rates and analyzes the long-term energy absorption behavior in chaotic systems under periodic driving.

Findings

Chaotic systems exhibit diffusive energy evolution under rapid periodic driving.

A prethermal state with minimal energy absorption exists before eventual heating.

In large systems, indefinite energy absorption or reaching infinite temperature occurs.

Abstract

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