Non-Weyl Resonance Asymptotics for Quantum Graphs
arXiv:1003.0051
Abstract
We consider the resonances of a quantum graph that consists of a compact part with one or more infinite leads attached to it. We discuss the leading term of the asymptotics of the number of resonances of in a disc of a large radius. We call a \emph{Weyl graph} if the coefficient in front of this leading term coincides with the volume of the compact part of . We give an explicit topological criterion for a graph to be Weyl. In the final section we analyze a particular example in some detail to explain how the transition from the Weyl to the non-Weyl case occurs.
29 pages, 2 figures