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

@article{Davies2010NonWeylAF, title={Non-Weyl asymptotics for quantum graphs with general coupling conditions}, author={E. B. Davies and Pavel Exner and Jiř{\'i} Lipovsk{\'y}}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2010}, volume={43}, pages={474013} }

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…

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