Star Graphs and Seba Billiards

Berkolaiko, G.; Bogomolny, E.B.; Keating, J.P.

HPL-BRIMS-2000-22

Keyword(s): graphs; spectral statistics; billiards

Abstract: We derive an exact expression for the two-point correlation function for quantum star graphs in the limit as the number of bonds tends to infinity. This turns out to be identical to the corresponding result for certain Seba billiards in the semiclassical limit. Reasons for this are discussed. The formula we derive is also shown to be equivalent to a series expansion for the form factor - the Fourier transform of the two-point correlation function - previously calculated using periodic orbit theory. Notes: G. Berkolaiko, Dept of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel E.B. Bogomolny, Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris-Sud, 91405 Orsay Cedex, France

24 Pages

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