Jiri Lipovsky
On the effective size of a non-Weyl graph
(522K, pdf)
ABSTRACT. We show how to find the coefficient by the leading term of the resonance asymptotics using the method of pseudo orbit expansion for quantum graphs which do not obey the Weyl asymptotics. For a non-Weyl graph we develop a method how to reduce the number of edges of a corresponding directed graph. With this method we prove bounds on the above coefficient depending on the structure of the graph for graphs with the same lengths of the internal edges. We explicitly find the positions of the resolvent resonances.