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Non-Weyl asymptotics for quantum graphs with general coupling conditions
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SYSNO ASEP 0350854 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Non-Weyl asymptotics for quantum graphs with general coupling conditions Author(s) Davies, E.B. (GB)
Exner, Pavel (UJF-V) RID, ORCID, SAI
Lipovský, Jiří (UJF-V)Source Title Journal of Physics A-Mathematical and Theoretical. - : Institute of Physics Publishing - ISSN 1751-8113
Roč. 43, č. 47 (2010), 474013/1-474013/16Number of pages 16 s. Language eng - English Country GB - United Kingdom Keywords KIRCHHOFFS RULE ; WIRES Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000284100400014 DOI 10.1088/1751-8113/43/47/474013 Annotation 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. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2011
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