Separation of particles leading either to decay or unlimited growth of energy in a driven stadium-like billiard

Abstract

Competition between the decay and growth of energy in a time-dependent stadium billiard is discussed with emphasis on the decay of the energy mechanism. A critical resonance velocity is identified as causing the separation between ensembles of high and low energy and a statistical investigation is performed using ensembles of initial conditions both above and below the resonance velocity. For high initial velocity, Fermi acceleration is inherent in the system. However, for low initial velocity, the resonance and stickiness hold the particles in a regular or quasi-regular regime near the fixed points, preventing them from exhibiting Fermi acceleration. Also, a transport analysis along the velocity axis is discussed to quantify the competition in the growth and decay of the energy, making use of the distributions of histograms of frequency, and we find that the energy decay is caused by the capture of the orbits by the resonant fixed points.