Departure of some parameter-dependent spectral statistics of irregular quantum graphs from Random Matrix Theory predictions
Chaotic Dynamics
2009-07-17 v1
Abstract
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)).
Keywords
Cite
@article{arxiv.0907.2794,
title = {Departure of some parameter-dependent spectral statistics of irregular quantum graphs from Random Matrix Theory predictions},
author = {Oleh Hul and Petr Seba and Leszek Sirko},
journal= {arXiv preprint arXiv:0907.2794},
year = {2009}
}
Comments
18 pages, 9 figures