Emergence of Quantum Ergodicity in Rough Billiards
Klaus M. Frahm, Dima L. Shepelyansky
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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