Statistical properties of resonance widths for open Quantum Graphs
Chaotic Dynamics
2007-05-23 v1
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.
Cite
@article{arxiv.nlin/0301021,
title = {Statistical properties of resonance widths for open Quantum Graphs},
author = {Tsampikos Kottos and Holger Schanz},
journal= {arXiv preprint arXiv:nlin/0301021},
year = {2007}
}
Comments
17 pages, 7 figures. submitted to Waves in Random Media, special issue for graphs