Spectral Statistics of the Rectangular Billiard with a Flux Line

The density of states of a rectangular billiard with an Aharonov–Bohm flux line in its center was calculated in the semiclassical approximation and was used for the calculation of the form factor in the diagonal approximation. The distribution of nearest level spacings and the form factor were calculated also numerically. For some values of the flux these were found to be close to the ones of the semi-Poisson statistics. The difference between the numerical results and the semiclassical ones were found to be much larger than for chaotic and for integrable systems within similar approximations. Possible reasons for these discrepancies are discussed.