We study scattering for the couple (A F ,A 0 ) of Schrödinger operators in L 2 (R 3 ) formally defined as A 0 =−Δ+αδ π javax.xml.bind.JAXBElement@35266ea2 and A F =−Δ+αδ π javax.xml.bind.JAXBElement@56dd5bc1 , α>0, where δ π javax.xml.bind.JAXBElement@4dbab1e is the Dirac δ-distribution supported on the deformed plane given by the graph of the compactly supported, Lipschitz continuous function F:R 2 →R and π 0 is the undeformed plane corresponding to the choice F≡0. We provide a Limiting Absorption Principle, show asymptotic completeness of the wave operators and give a representation formula for the corresponding Scattering Matrix S F (λ). Moreover we show that, as F→0, ‖S F (λ)−1‖ B(L javax.xml.bind.JAXBElement@b81c41d (S javax.xml.bind.JAXBElement@dd4f8b1 )) 2 =O(∫ R javax.xml.bind.JAXBElement@316bb999 dx|F(x)| γ ), 0<γ<1.

Scattering from local deformations of a semitransparent plane

Cacciapuoti, Claudio
;
Posilicano, Andrea
2019-01-01

Abstract

We study scattering for the couple (A F ,A 0 ) of Schrödinger operators in L 2 (R 3 ) formally defined as A 0 =−Δ+αδ π javax.xml.bind.JAXBElement@35266ea2 and A F =−Δ+αδ π javax.xml.bind.JAXBElement@56dd5bc1 , α>0, where δ π javax.xml.bind.JAXBElement@4dbab1e is the Dirac δ-distribution supported on the deformed plane given by the graph of the compactly supported, Lipschitz continuous function F:R 2 →R and π 0 is the undeformed plane corresponding to the choice F≡0. We provide a Limiting Absorption Principle, show asymptotic completeness of the wave operators and give a representation formula for the corresponding Scattering Matrix S F (λ). Moreover we show that, as F→0, ‖S F (λ)−1‖ B(L javax.xml.bind.JAXBElement@b81c41d (S javax.xml.bind.JAXBElement@dd4f8b1 )) 2 =O(∫ R javax.xml.bind.JAXBElement@316bb999 dx|F(x)| γ ), 0<γ<1.
2019
http://www.elsevier.com/inca/publications/store/6/2/2/8/8/6/index.htt
Kreĭn's resolvent formulae; Point interactions supported by unbounded hypersurfaces; Scattering theory; Analysis; Applied Mathematics
Cacciapuoti, Claudio; Fermi, Davide; Posilicano, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2076072
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