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

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

2009-07-16

arxiv.org/abs/0907.2794v1

Phys. Rev. E 79, 066204 (2009)

Nonlinear Sciences

Chaotic Dynamics

18 pages, 9 figures

Scientific paper

10.1103/PhysRevE.79.066204

Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions of level curvatures and avoided crossing gaps are calculated. The numerical results are compared with the predictions of Random Matrix Theory (RMT) for Gaussian Orthogonal Ensemble (GOE) and for coupled GOE matrices. The application of coupled GOE matrices was justified by studying localization phenomena in graphs' wave functions Psi(x) using the Inverse Participation Ratio (IPR) and the amplitude distribution P(Psi(x)).

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