NonWeyl Resonance Asymptotics for Quantum Graphs
Abstract
We consider the resonances of a quantum graph $\mathcal G$ 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 $\mathcal G$ in a disc of a large radius. We call $\mathcal G$ a \emph{Weyl graph} if the coefficient in front of this leading term coincides with the volume of the compact part of $\mathcal G$. 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 nonWeyl case occurs.
 Publication:

arXiv eprints
 Pub Date:
 March 2010
 arXiv:
 arXiv:1003.0051
 Bibcode:
 2010arXiv1003.0051D
 Keywords:

 Mathematics  Spectral Theory;
 Primary 34B45;
 Secondary 35B34;
 47E05
 EPrint:
 29 pages, 2 figures