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Numerical investigation of regimes of Wigner and Shnirelman ergodicity in rough billiards. (English) Zbl 1062.37504

Summary: We study numerically regimes of Wigner and Shnirelman ergodicity in rough half-circular billiards. We show that in the regime of Wigner ergodicity eigenstates are extended over the whole energy surface but have a strongly peaked nonergodic structure. In the regime of Shnirelman ergodicity the eigenstates are ergodically distributed along the energy surface. The Shannon width of the eigenstate distributions is calculated to estimate quantitatively their spreads. We show that in both regimes the amplitude distribution \(P(\psi)\) is well approximated by a Gaussian distribution.

MSC:

37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
81Q50 Quantum chaos
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