Coupling in the singular limit of thin quantum waveguides

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dc.creatorAlbeverio, Sergio
dc.creatorCacciapuoti, Claudio
dc.creatorFinco, Domenico
dc.date2006-11-22
dc.date2007-02-23
dc.date.accessioned2026-07-07T07:48:09Z
dc.date.available2026-07-07T07:48:09Z
dc.descriptionWe analyze the problem of approximating a smooth quantum waveguide with a quantum graph. We consider a planar curve with compactly supported curvature and a strip of constant width around the curve. We rescale the curvature and the width in such a way that the strip can be approximated by a singular limit curve, consisting of one vertex and two infinite, straight edges, i.e. a broken line. We discuss the convergence of the Laplacian, with Dirichlet boundary conditions on the strip, in a suitable sense and we obtain two possible limits: the Laplacian on the line with Dirichlet boundary conditions in the origin and a non trivial family of point perturbations of the Laplacian on the line. The first case generically occurs and corresponds to the decoupling of the two components of the limit curve, while in the second case a coupling takes place. We present also two families of curves which give rise to coupling.
dc.description20 pages, no figures. Minor misprint corrected, two references added
dc.identifierhttps://arxiv.org/abs/math-ph/0611059
dc.identifierhttp://arxiv.org/abs/math-ph/0611059
dc.identifierJ. Math. Phys., 48 (2007)
dc.identifierdoi:10.1063/1.2710197
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124400
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject81Q10, 47A10, 35P05
dc.titleCoupling in the singular limit of thin quantum waveguides
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