Energy diffusion and absorption in chaotic systems with rapid periodic driving

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 expl...

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Bibliographic Details
Published inarXiv.org
Main Authors Hodson, Wade, Jarzynski, Christopher
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.02.2021
Subjects
Chaos theory
Diffusion rate
Energy
Energy absorption
Energy distribution
Fokker-Planck equation
Hamiltonian functions
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ISSN2331-8422

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Summary: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.
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SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422