Davies, E. Brian; Exner, Pavel; Lipovský, Jiří Non-Weyl asymptotics for quantum graphs with general coupling conditions. (English) Zbl 1204.81078 J. Phys. A, Math. Theor. 43, No. 47, Article ID 474013, 16 p. (2010). Summary: 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. Cited in 16 Documents MSC: 81Q35 Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices PDFBibTeX XMLCite \textit{E. B. Davies} et al., J. Phys. A, Math. Theor. 43, No. 47, Article ID 474013, 16 p. (2010; Zbl 1204.81078) Full Text: DOI arXiv