Semiclassical Quantization of Billiards with Mixed Boundary Conditions

Details Semiclassical Quantization of Billiards with Mixed Boundary Conditions Semiclassical Quantization of Billiards with Mixed Boundary Conditions

1995-02-19

arxiv.org/abs/chao-dyn/9502015v2

Nonlinear Sciences

Chaotic Dynamics

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Scientific paper

10.1088/0305-4470/28/17/032

The semiclassical theory for billiards with mixed boundary conditions is developed and explicit expressions for the smooth and the oscillatory parts of the spectral density are derived. The parametric dependence of the spectrum on the boundary condition is shown to be a very useful diagnostic tool in the semiclassical analysis of the spectrum of billiards. It is also used to check in detail some recently proposed parametric spectral statistics. The methods are illustrated in the analysis of the spectrum of the Sinai billiard and its parametric dependence on the boundary condition on the dispersing arc.

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