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Spectral properties of quantized barrier billiards

Jan Wiersig
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Abstract

The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions, number variances, spectral form factors, and the level dynamics is carried out. For a special member of the billiard family, the form factor is calculated analytically for small arguments in the diagonal approximation. All results together are consistent with the so-called semi-Poisson statistics.

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Jan Wiersig. 2002-02-01. Spectral properties of quantized barrier billiards. https://doi.org/10.1103/physreve.65.046217

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