Non-Weyl asymptotics for quantum graphs with general coupling conditions

Details Non-Weyl asymptotics for quantum graphs with general coupling conditions Non-Weyl asymptotics for quantum graphs with general coupling conditions

2010-04-06

arxiv.org/abs/1004.0856v2

Physics

Mathematical Physics

minor changes, to appear in Pierre Duclos memorial issue of J. Phys. A: Math. Theor

Scientific paper

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 case of Kirchhoff or anti-Kirchhoff conditions, while for graphs without permutation numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight helping to understand what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with nonequal edge weights.

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