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Non-Weyl asymptotics for quantum graphs with general coupling conditions
- 1.0350854 - ÚJF 2011 RIV GB eng J - Journal Article
Davies, E.B. - Exner, Pavel - Lipovský, Jiří
Non-Weyl asymptotics for quantum graphs with general coupling conditions.
Journal of Physics A-Mathematical and Theoretical. Roč. 43, č. 47 (2010), 474013/1-474013/16. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : KIRCHHOFFS RULE * WIRES
Subject RIV: BE - Theoretical Physics
Impact factor: 1.641, year: 2010
Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.
Permanent Link: http://hdl.handle.net/11104/0190743
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