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Abstracts
In this note we explain the method how to find the resonance condition on quantum graphs, which is called pseudo-orbit expansion. In three examples with standard coupling we show in detail how to obtain the resonance condition. We focus on non-Weyl graphs, i.e. the graphs which have fewer resonances than expected. For these graphs we explain benefits of the method of "deleting edges" for simplifying the graph.
Discipline
Journal
Year
Volume
Issue
Pages
968-973
Physical description
Dates
published
2015-12
Contributors
author
- Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03 Hradec Králové, Czechia
References
- [1] P. Exner, J. Lipovský, Equivalence of resolvent and scattering resonances on quantum graphs, in Adventures in Mathematical Physics (Proc., Cergy-Pontoise 2006), Eds. F. Germinet, P.D. Hislop, Vol. 447, Am. Math. Soc., Providence, RI 2007, p. 73, doi: 10.1090/conm/447
- [2] T. Kottos, U. Smilansky, J. Phys. A Math. Gen. 36, 3501 (2003), doi: 10.1088/0305-4470/36/12/337
- [3] T. Kottos, H. Schanz, Waves Rand. Media 14, S91 (2004), doi: 10.1088/0959-7174/14/1/013
- [4] R. Band, J.M. Harrison, C.H. Joyner, J. Phys. A Math. Theor. 45, 325204 (2012), doi: 10.1088/1751-8113/45/32/325204
- [5] J. Lipovský, arXiv:1507.04176 [math-ph] (2015)
- [6] E.B. Davies, A. Pushnitski, Anal. PDE 4, 729 (2011), doi: 10.2140/apde.2011.4.729
- [7] E.B. Davies, P. Exner, J. Lipovský, J. Phys. A Math. Theor. 43, 474013 (2010), doi: 10.1088/1751-8113/43/47/474013
- [8] P. Exner, J. Lipovský, Phys. Lett. A 375, 805 (2011), doi: 10.1016/j.physleta.2010.12.042
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv128n602kz