Transport Properties of a Classical One-Dimensional Kicked Billiard Model

Abstract

We study a classical 1-dimensional kicked billiard model and investigate its transport behavior. The roles played by the two system parameters α and K, governing the direction and strength of the kick, respectively, are found to be quite crucial. For the perturbations which are not strong, i.e. K < 1, we find that as the phase parameter α changes within its range of interest from -π/2 to π/2, the phase space is in turn characterized by the structure of a prevalently connected stochastic web (-π/2 ⩽ α < 0), local stochastic webs surrounded by a stochastic sea (0 < α < π/2) and the global stochastic sea (α = π/2). Extensive numerical investigations also indicate that the system's transport behavior in the irregular regions of the phase space for K < 1 has a dependence on the system parameters and the transport coefficient D can be expressed as D ≈ D0(α)Kf(α). For strong kicks, i.e. K ≫ 1, the phase space is occupied by the stochastic sea, and the transport behavior of the system seems to be similar to that of the kicked rotor and independent of α.