Topological Resonances on Quantum Graphs

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 estimate of the dimension of this semi-algebraic set, in particular in terms of the girth of the graph. The case of trees is also discussed.
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https://hal.archives-ouvertes.fr/hal-01298494
Contributor : Yves Colin de Verdière <>
Submitted on : Tuesday, February 27, 2018 - 8:28:41 AM
Last modification on : Wednesday, September 26, 2018 - 10:44:03 AM

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  • HAL Id : hal-01298494, version 2
  • ARXIV : 1604.01732

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Yves Colin de Verdìère, Francoise Truc. Topological Resonances on Quantum Graphs. Annales Henri Poincaré, Springer Verlag, In press. ⟨hal-01298494v2⟩

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