Statistical properties of resonance widths for open Quantum Graphs
arXiv:nlin/0301021 · doi:10.1088/0959-7174/14/1/013
Abstract
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyze the statistical properties of the resonance widths and compare our results with the predictions of Random Matrix Theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.
17 pages, 7 figures. submitted to Waves in Random Media, special issue for graphs
References in corpus (26)
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
- Observation of resonance trapping in an open microwave cavity
- Chaotic Scattering on Graphs
- Quantum Graphs: A simple model for Chaotic Scattering
- On the level spacing distribution in quantum graphs
- Contact interactions on graph superlattices
- S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances
- Spectral determinant on quantum graphs
- Parametric Correlations of Scattering Phase Shifts and Fluctuations of Delay Times in Few-Channel Chaotic Scattering
- Periodic-Orbit Theory of Anderson Localization on Graphs
- Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances
- Effective Coupling for Open Billiards
- Spectral statistics for unitary transfer matrices of binary graphs
- Star graphs and Seba billiards
- Parametric Correlations of Phase Shifts and Statistics of Time Delays in Quantum Chaotic Scattering: Crossover between Unitary and Orthogonal Symmetries
- The Leading Off-Diagonal Correction to the Form Factor of Large Graphs
- Transmission through quantum networks
- Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect
- Scattering theory on graphs
- Transport and dynamics on open quantum graphs
- Quantum Graphs: A model for Quantum Chaos
- Classical dynamics on graphs
- Eigenstate Structure in Graphs and Disordered Lattices
- Spectral Statistics for Quantum Graphs: Periodic Orbits and Combinatorics
- Scattering theory on graphs (2): the Friedel sum rule
Cited by in corpus (11)
- Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
- Chaotic Scattering on Individual Quantum Graphs
- Perfect Absorption in Complex Scattering Systems with or without Hidden Symmetries
- Universal Chaotic Scattering on Quantum Graphs
- Dynamics of nodal points and the nodal count on a family of quantum graphs
- On the Effective Size of a Non-Weyl Graph
- A spectral duality in graphs and microwave networks
- Pseudo orbit expansion for the resonance condition on quantum graphs and the resonance asymptotics
- Nonlinearity-induced Scattering Zero Degeneracies for Spectral Management of Coherent Perfect Absorption in Complex Systems
- Recovering quantum graph spectrum from vertex data
- Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation