Diffusion Phenomena in a Mixed Phase Space
Statistical Mechanics
2020-01-29 v1 Chaotic Dynamics
Abstract
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.
Cite
@article{arxiv.1907.11702,
title = {Diffusion Phenomena in a Mixed Phase Space},
author = {Matheus S. Palmero and Gabriel I. Díaz and Peter V. E. McClintock and Edson D. Leonel},
journal= {arXiv preprint arXiv:1907.11702},
year = {2020}
}
Comments
Submitted to Chaos