Emergence of Quantum Ergodicity in Rough Billiards

Budker Institute of Nuclear Physics, Novo-Nikolaevsk, Novosibirsk, Russia
Physical Review Letters (Impact Factor: 7.51). 02/1997; 79(10). DOI: 10.1103/PhysRevLett.79.1833
Source: arXiv


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. Comment: revtex, 4 pages, 4 figures

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    • "p 2 when x is inside, and H(x, p) = ∞ when x is outside. If (for pedagogical simplicity) we take the billiard to be nearly circular with radius L (e.g, a stadium with a short straight segment [7], or a circle with rough walls [8]), and the bouncing ball to have energy E = "
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