Aspects of diffusion in the stadium billiard

Abstract

We perform a detailed numerical study of diffusion in the $\epsilon$ stadium of Bunimovich, and propose an empirical model of the local and global diffusion for various values of $\epsilon$ with the following conclusions: (i) the diffusion is normal for all values of $\epsilon \le (0.3)$ and all initial conditions, (ii) the diffusion constant is a parabolic function of the momentum (i.e., we have inhomogeneous diffusion), (iii) the model describes the diffusion very well including the boundary effects, (iv) the approach to the asymptotic equilibrium steady state is exponential, (v) the so-called random model (Robnik et al., 1997) is confirmed to apply very well, (vi) the diffusion constant extracted from the distribution function in momentum space and the one derived from the second moment agree very well. The classical transport time, an important parameter in quantum chaos, is thus determined.

arXiv comment12 pages, 14 figures, 1 table

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• Structure, size, and statistical properties of chaotic components in a mixed-type Hamiltonian system
• Spectral form factors and dynamical localization
• Diffusion Phenomena in a Mixed Phase Space
• Discussing a transition from bounded to unbounded energy in a time-dependent billiard
• Symmetry breaking in time-dependent billiards