Non-Weyl asymptotics for quantum graphs with general coupling conditions
Abstract
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.
Keywords
Cite
@article{arxiv.1004.0856,
title = {Non-Weyl asymptotics for quantum graphs with general coupling conditions},
author = {E. Brian Davies and Pavel Exner and Jiri Lipovsky},
journal= {arXiv preprint arXiv:1004.0856},
year = {2019}
}
Comments
minor changes, to appear in Pierre Duclos memorial issue of J. Phys. A: Math. Theor