Periodic orbit theory and the statistical analysis of scaling quantum graph spectra.
- Author(s): Dabaghian, Yu
- et al.
Published Web Locationhttp://link.aps.org/abstract/PRE/v75/e056214
The explicit solution to the spectral problem of quantum graphs found recently by Dabaghian and Blümel [Phys. Rev. E 68, 055201(R) (2003); 70, 046206 (2004); JETP Lett. 77, 530 (2003)] is used to produce an exact periodic orbit theory description for the probability distributions of spectral statistics, including the distribution for the nearest neighbor separations sn = kn - kn-1, and the distribution of the spectral oscillations around the average, deltakn=kn - kn.