DISPLACEMENT EFFECTS ON FERMI ACCELERATION IN RANDOMIZED DRIVEN BILLIARDS

摘要

Fermi acceleration of an ensemble of non-interacting particles evolving in a stochastic Fermi-Ulam model (FUM) and the phase randomized harmonically driven periodic Lorentz gas is investigated. As shown in [A. K. Karns, P. K. Papachristou, F. K. Diakonos, V. Constantoudis and P. Schmelcher, Phys. Rev. Lett. 97, 194102 (2006)], the static wall approximation, which ignores scatterer displacement upon collision, leads to a substantial underestimation of the mean energy gain per collision. Herein we clarify the mechanism leading to the increased acceleration, through the investigation of a randomized FUM, comprising one fixed and one moving wall oscillating according to a sawtooth time-law. Moreover, it is shown that the presence of a particular asymmetry of the driving function leads to a different particle energy gain compared to the one observed when a symmetric driving law is considered. Furthermore, the impact of scatterer displacement upon collision on the acceleration of particles in the case of a harmonically driven phase randomized Lorentz gas is investigated in terms of a Markov process in momentum space. Generalizing the recently introduced hopping wall approximation (HWA) for application in the Lorentz gas, the time-evolving distribution of particle speeds is obtained. The analysis reveals that the underestimation made by the static approximation in both the Lorentz gas and the FUM, assuming a harmonic driving, is the same.