Emergence of Quantum Ergodicity in Rough Billiards

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Abstract
By analytical mapping of the eigenvalue problem in rough billiards onto a band random matrix model, a new regime of Wigner ergodicity is found. There, the eigenstates are extended over the whole energy surface but have a strongly peaked nonergodic structure. At the same time the level spacing statistics is still given by the Wigner-Dyson distribution.
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