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2015 | 128 | 6 | 968-973
Article title

Pseudo-Orbit Expansion for the Resonance Condition on Quantum Graphs and the Resonance Asymptotics

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EN
Abstracts
EN
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.
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EN
Year
Volume
128
Issue
6
Pages
968-973
Physical description
Dates
published
2015-12
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
YADDA identifier
bwmeta1.element.bwnjournal-article-appv128n602kz
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