The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with a barrier in the centre can be reduced to the investigation of a certain unitary matrix. Under heuristic assumptions this matrix is substituted by a special low-complexity random unitary matrix of independent interest. The main results of the paper are (i) spectral statistics of such billiards is insensitive to the barrier height and (ii) it is well described by the semi-Poisson distributions.
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Uniwersytet Jagiellonski, Mark Kac Complex Syst Res Ctr, PL-30059 Krakow, PolandUniwersytet Jagiellonski, Mark Kac Complex Syst Res Ctr, PL-30059 Krakow, Poland
Cappellini, Valerio
Sommers, Hans-Juergen
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Univ Duisburg Essen, Fachbereich Phys, D-47048 Duisburg, GermanyUniwersytet Jagiellonski, Mark Kac Complex Syst Res Ctr, PL-30059 Krakow, Poland
Sommers, Hans-Juergen
Bruzda, Wojciech
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Uniwersytet Jagiellonski, Inst Fiz Smoluchowskiego, PL-30059 Krakow, PolandUniwersytet Jagiellonski, Mark Kac Complex Syst Res Ctr, PL-30059 Krakow, Poland
Bruzda, Wojciech
Zyczkowski, Karol
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Uniwersytet Jagiellonski, Inst Fiz Smoluchowskiego, PL-30059 Krakow, Poland
Polish Akad Nauk, Ctr Fiz Teoretycznej, PL-02668 Warsaw, PolandUniwersytet Jagiellonski, Mark Kac Complex Syst Res Ctr, PL-30059 Krakow, Poland