Star graphs and Seba billiards

Details Star graphs and Seba billiards Star graphs and Seba billiards

2000-10-26

arxiv.org/abs/nlin/0010045v1

J. Phys. A 34 (3) 335-350 (2001)

Nonlinear Sciences

Chaotic Dynamics

24 pages, 3 figures, submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/34/3/301

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.

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