Periodic orbit theory and the statistical analysis of scaling quantum graph spectra.
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.
Dabaghian
Yu
Y
Department of Physiology, Keck Center for Integrative Neuroscience, University of California, San Francisco, California 94143-0444, USA. yura@phy.ucsf.edu