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Diffusion Phenomena in a Mixed Phase Space

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>7/01/2020
Publication statusE-pub ahead of print
Early online date7/01/20
Original languageEnglish


We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in phase space, the method of images and use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with chaotic seas, invariant tori and Kolmogorov-Arnold-Moser (KAM) islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory. The procedure can readily be extended to other systems including time-dependent billiards.

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Copyright 2019 American Institute of Physics. The following article appeared in Chaos, ??, 2019 and may be found at http://dx.doi.org/[add doi] This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.