Topological Resonances on Quantum Graphs
Mathematical Physics
2016-04-07 v1 Analysis of PDEs
Combinatorics
math.MP
Spectral Theory
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.
Cite
@article{arxiv.1604.01732,
title = {Topological Resonances on Quantum Graphs},
author = {Yves Colin de Verdìère and Francoise Truc},
journal= {arXiv preprint arXiv:1604.01732},
year = {2016}
}
Comments
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