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. The 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.
|Translated title of the contribution||Star graphs and Seba billiards|
|Pages (from-to)||335 - 350|
|Journal||Journal of Physics A: Mathematical and General|
|Publication status||Published - 26 Jan 2001|
Bibliographical notePublisher: IOP Publishing Ltd
Other identifier: IDS number 400FR