Departure of some parameter-dependent spectral statistics of irregular quantum graphs from Random Matrix Theory predictions

摘要

Parameter-dependent statistical properties of spectra of totally connectedirregular quantum graphs with Neumann boundary conditions are studied. Theautocorrelation functions of level velocities c(x) and c(w,x) as well as thedistributions of level curvatures and avoided crossing gaps are calculated. Thenumerical results are compared with the predictions of Random Matrix Theory(RMT) for Gaussian Orthogonal Ensemble (GOE) and for coupled GOE matrices. Theapplication of coupled GOE matrices was justified by studying localizationphenomena in graphs' wave functions Psi(x) using the Inverse ParticipationRatio (IPR) and the amplitude distribution P(Psi(x)).