Barrier billiard and random matrices

被引:5
|
作者
Bogomolny, Eugene [1 ]
机构
[1] Univ Paris Saclay, LPTMS, CNRS, F-91405 Orsay, France
关键词
barrier billiards; random matrices; spectral statistics; SEMICLASSICAL QUANTIZATION; ROOT-N; STATISTICS; SPECTRA; TRANSITION; POLYGONS; SYSTEMS;
D O I
10.1088/1751-8121/ac3da6
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页数:20
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