On geometric perturbations of critical Schrödinger operators with a surface interaction

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dc.creatorExner, P.
dc.creatorFraas, M.
dc.date2009-01-09
dc.date.accessioned2026-07-07T12:27:57Z
dc.date.available2026-07-07T12:27:57Z
dc.descriptionWe study singular Schrodinger operators with an attractive interaction supported by a closed smooth surface A in R^3 and analyze their behavior in the vicinity of the critical situation where such an operator has empty discrete spectrum and a threshold resonance. In particular, we show that if A is a sphere and the critical coupling is constant over it, any sufficiently small smooth area preserving radial deformation gives rise to isolated eigenvalues. On the other hand, the discrete spectrum may be empty for general deformations. We also derive a related inequality for capacities associated with such surfaces.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/0901.1148
dc.identifierhttp://arxiv.org/abs/0901.1148
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215386
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subjectQuantum Physics
dc.subject81V99
dc.titleOn geometric perturbations of critical Schrödinger operators with a surface interaction
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