Topological Resonances on Quantum GraphsReport as inadecuate

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1 IF - Institut Fourier

Abstract : In this paper, we try to put the results of Smilansky and al. on -Topological resonances- on a mathematical basis.A key role in the asymptotic of resonances near the real axis for Quantum Graphs is played by the set of metrics for which there exists compactly supported eigenfunctions. We give several estimateof the dimension of this semi-algebraic set, in particular in terms of the girth of the graph. The case oftrees is also discussed.

Keywords : resonances Quantum graphs cycles in graphs

Author: Yves Colin de Verdìère - Francoise Truc -



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