Počet záznamů: 1

Non-Weyl asymptotics for quantum graphs with general coupling conditions

  1. 1.
    0350854 - UJF-V 2011 RIV GB eng J - Článek v odborném periodiku
    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
    Grant CEP: GA MŠk LC06002
    Výzkumný záměr: CEZ:AV0Z10480505
    Klíčová slova: KIRCHHOFFS RULE * WIRES
    Kód oboru RIV: BE - Teoretická fyzika
    Impakt faktor: 1.641, rok: 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.
    Trvalý link: http://hdl.handle.net/11104/0190743