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Emergence of Quantum Ergodicity in Rough Billiards

Klaus M. Frahm·Dima L. Shepelyansky
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Abstract

By analytical mapping of the eigenvalue problem in rough billiards on to 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 structure. The results of numerical simulations and implications for level statistics are also discussed.

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Klaus M. Frahm, Dima L. Shepelyansky. 1997-02-14. Emergence of Quantum Ergodicity in Rough Billiards. https://doi.org/10.1103/physrevlett.79.1833

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