Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

Abstract

Some statistical properties related to the diffusion in energy for an ensemble of classical particles in a bouncing ball model are studied. The particles are confined to bounce between two rigid walls. One of them is fixed while the other oscillates. The dynamics is described by a two dimensional nonlinear map for the velocity of the particle and time at the instant of the collision. Two different types of change of momentum are considered: (i) periodic due to a sine function and; (ii) stochastic. For elastic collisions case (i) leads to finite diffusion in energy while (ii) produces unlimited diffusion. On the other hand, inelastic collisions yield either (i) and (ii) to have limited diffusion. Scaling arguments are used to investigate some properties of the transport coefficient in the chaotic low energy region. Scaling exponents are also obtained for both conservative and dissipative case for cases (i) and (ii). We show that the parameter space has complicated structures either in Lyapunov as well as period coordinates. When stochasticity is introduced in the dynamics, we observed the destruction of the parameter space structures.