2-point spectral correlations for the square billiard
By: J.P. Keating, R.D. Connors.
Contributors: Connors, R. D.; Hewlett-Packard Laboratories.
Series: [Technical report] / HP Laboratories Bristol. Basic Research Institute in the Mathematical Sciences -- HPL-BRIMS-96-29.; BRIMS technical report -- HPL-BRIMS-96-29.
Publisher: Hewlett Packard
Published: 1996
Place of publication: Bristol [England]
Language: eng
Number of pages: 21
Subjects: Poisson processes; Spectral theory (Mathematics)
Other titles: Two-point spectral correlations for the square billiard.
Description: Abstract: "We investigate the 2-point correlations in the quantum spectrum of the square billiard. This system is unusual in that the degeneracy of the energy levels increases in the semiclassical limit in such a way that the average level separation is not given by the inverse of the mean density of states. Hence, for example, the standard level spacings distribution does not tend to the Poissonian limit expected for integrable systems. We here calculate the leading-order asymptotic form of a degeneracy-weighted 2-point correlation function using a combination of probabilistic techniques and classical number theory. The result exhibits number-theoretical fluctuations about a mean which is a sum of two terms: one having the usual (constant) Poissonian form and the second representing a small correction which decays as the inverse of the correlation distance. This is confirmed by numerical computations."
Notes: Cover title.

"December, 1996."

Includes bibliographical references.