2003/01/18 by Tsampikos Kottos, Holger Schanz · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Quantum Information and Cryptography #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #nlin.CD
paper · pdf · doi:10.1088/0959-7174/14/1/013
published as Waves Random Media 14 (2004) S91-S105 · 17 pages, 7 figures. submitted to Waves in Random Media, special issue for graphs
arxiv created 2003/01/18 · openalex publication_date 2004/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.