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

• Authors: J. Lipovský
• Languages of publication: 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.

Keywords

EN

03.65.Ge; 03.65.Nk; 02.10.Ox

Discipline

• 03.65.Nk: Scattering theory
• 02.10.Ox: Combinatorics; graph theory
• 03.65.Ge: Solutions of wave equations: bound states

• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 128
• Issue: 6
• Pages: 968-973

Dates

published

2015-12

Contributors

author

J. Lipovský

• 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

Identifiers

DOI

10.12693/APhysPolA.128.968