Minimal Fermi model

Abstract

In this work, we consider the simple model for Fermi acceleration of a particle between two periodically oscillating walls, The law of wall movement is continuous but not smooth. Exact mapping for this system has been obtained. A fractal saet of trajectories with infinitely increasing speed is shown to exist. The main characteristic of such trajectories are discussed. A comparison with heigh-energy approach has been carried out. Quanlitative differences in behavior of exact and approximate description have been found. For example, in heigh-energy approach, there are no trajectories with unlimited speed increase.