On the Effective Size of a Non-Weyl Graph

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. Through this method we prove bounds on the above coefficient depending on the structure of the graph for graphs with the same lengths of internal edges. We explicitly find the positions of the resolvent resonances.

22 pages, 13 figures

References in corpus (2)

• Statistical properties of resonance widths for open Quantum Graphs
• Pseudo orbit expansion for the resonance condition on quantum graphs and the resonance asymptotics

Cited by in corpus (7)

• Non-Weyl Microwave Graphs
• Asymptotics of resonances induced by point interactions
• Quantum graphs and microwave networks as narrow band filters for quantum and microwave devices
• Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics
• Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks
• Coupled unidirectional chaotic microwave graphs
• Scattering resonances of large weakly open quantum graphs