Phase Space Interpretation of Exponential Fermi Acceleration
Abstract
Recently, the occurrence of exponential Fermi acceleration has been reported in a rectangular billiard with an oscillating bar inside [K. Shah, D. Turaev, and V. Rom-Kedar, Phys. Rev. E {\bf 81}, 056205 (2010)]. In the present work, we analyze the underlying physical mechanism and show that the phenomenon can be understood as a sequence of highly correlated motions, consisting of alternating phases of free propagation and motion along the invariant spanning curves of the well-known one-dimensional Fermi-Ulam model. The key mechanism for the occurrence of exponential Fermi acceleration can be captured in a random walk model in velocity space with step width proportional to the velocity itself. The model reproduces the occurrence of exponential Fermi acceleration and provides a good ab initio prediction of the value of the growth rate including its full parameter-dependency. Our analysis clearly points out the requirements for exponential Fermi acceleration, thereby opening the perspective of finding other systems exhibiting this unusual behaviour.
Cite
@article{arxiv.1107.3509,
title = {Phase Space Interpretation of Exponential Fermi Acceleration},
author = {Benno Liebchen and Robert Büchner and Christoph Petri and Fotis K. Diakonos and Florian Lenz and Peter Schmelcher},
journal= {arXiv preprint arXiv:1107.3509},
year = {2013}
}