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Berry-Robnik level statistics in a smooth billiard system

Tomaz Prosen
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Abstract

Berry-Robnik level spacing distribution is demonstrated clearly in a generic quantized plane billiard for the first time. However, this ultimate semi-classical distribution is found to be valid only for extremely small semi-classical parameter (effective Planck's constant) where the assumption of statistical independence of regular and irregular levels is achieved. For sufficiently larger semiclassical parameter we find (fractional power-law) level repulsion with phenomenological Brody distribution providing an adequate global fit.

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Tomaz Prosen. 1998-03-27. Berry-Robnik level statistics in a smooth billiard system. https://doi.org/10.1088/0305-4470%2F31%2F34%2F005

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