Quantization of Sinai's Billiard - A Scattering Approach

Details Quantization of Sinai's Billiard - A Scattering Approach Quantization of Sinai's Billiard - A Scattering Approach

1995-02-25

arxiv.org/abs/chao-dyn/9502019v1

Nonlinear Sciences

Chaotic Dynamics

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Scientific paper

We obtained the spectrum of the Sinai billiard as the zeroes of a secular equation, which is based on the scattering matrix of a related scattering problem. We show that this quantization method provides an efficient numerical scheme, and its implementation for the present case gives a few thousands of levels without encountering any serious difficulty. We use the numerical data to check some approximations which are essential for the derivation of a semiclassical quantization method based also on this scattering approach.

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