Departure of some parameter-dependent spectral statistics of irregular quantum graphs from Random Matrix Theory predictions
arXiv:0907.2794 · doi:10.1103/PhysRevE.79.066204
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)).
18 pages, 9 figures
References in corpus (19)
- Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
- Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
- Experimental simulation of quantum graphs by microwave networks
- On the level spacing distribution in quantum graphs
- Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
- Scars on quantum networks ignore the Lyapunov exponent
- Coupled Microwave Billiards as a Model for Symmetry Breaking
- Parametric Conductance Correlation for Irregularly Shaped Quantum Dots
- Quantum Graphs: A model for Quantum Chaos
- Index theorems for quantum graphs
- Universality in quantum parametric correlations
- Eigenstate Structure in Graphs and Disordered Lattices
- Localization on a quantum graph with a random potential on the edges
- Quantum ergodicity for graphs related to interval maps
- Nonuniversality in level dynamics
- Parametric Spectral Correlations of Disordered Systems in the Fourier Domain
- On "Universal" Correlations in Disordered and Chaotic Systems
- Parametric correlation of Coulomb blockade conductance peaks in chaotic quantum dots
- Parametric Statistics of Individual Energy Levels in Random Hamiltonians
Cited by in corpus (7)
- Spectral Properties of Directed Random Networks with Modular Structure
- Quantum chaos and level dynamics
- Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance
- Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs
- Coupled unidirectional chaotic microwave graphs
- Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
- Families of isospectral and isoscattering quantum graphs