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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