# 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}
}
• Published 6 April 2010
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
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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