Abstract
We study numerically regimes of Wigner and Shnirelman ergodicity (K M Frahm and D L Shepelyansky 1997 Phys. Rev. Lett. 79 1833) 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(ψ) is well approximated by a Gaussian distribution.
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