Statistical properties of resonance widths for open Quantum Graphs

Details Statistical properties of resonance widths for open Quantum Graphs Statistical properties of resonance widths for open Quantum Graphs

2003-01-18

arxiv.org/abs/nlin/0301021v1

Waves Random Media 14 (2004) S91-S105

Nonlinear Sciences

Chaotic Dynamics

17 pages, 7 figures. submitted to Waves in Random Media, special issue for graphs

Scientific paper

10.1088/0959-7174/14/1/013

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.

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