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 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.
Citation
E. Brian Davies. Alexander Pushnitski. "Non-Weyl resonance asymptotics for quantum graphs." Anal. PDE 4 (5) 729 - 756, 2011. https://doi.org/10.2140/apde.2011.4.729
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