Diffusion phenomena in a mixed phase space - Palmero, Matheus S. [UNESP]; Díaz, Gabriel I.; McClintock, Peter V. E.; Leonel, Edson D. [UNESP] (AIP Publishing, 2020)
We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in a phase space, the method of images, and the 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 islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory.