Scattering from local deformations of a semitransparent plane

DOI10.1016/j.jmaa.2018.12.045zbMath1410.81033arXiv1807.07916OpenAlexW2884690708WikidataQ128738813 ScholiaQ128738813MaRDI QIDQ1733781

Andrea Posilicano, Davide Fermi, Claudio Cacciapuoti

Publication date: 21 March 2019

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.07916

zbMATH Keywords

scattering theoryKreĭn's resolvent formulaepoint interactions supported by unbounded hypersurfaces

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Lipschitz (Hölder) classes (26A16) Spectrum, resolvent (47A10) (S)-matrix theory, etc. in quantum theory (81U20)

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Cites Work

• Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces
• Upper bound for the number of bound states induced by the curvature of singular potential
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• Resolvent estimates for a sum of tensor products with applications to the spectral theory of differential operators
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• Generalized interactions supported on hypersurfaces
• Laplacians with singular perturbations supported on hypersurfaces
• Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane
• The limiting absorption principle for partial differential operators
• Bound states due to a strong   interaction supported by a curved surface
• Relative-Zeta and Casimir Energy for a Semitransparent Hyperplane Selecting Transverse Modes
• Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
• The Method of Potential Operators for Anisotropic Helmholtz Operators on Domains with Smooth Unbounded Boundaries
• Scattering by local deformations of a straight leaky wire
• A Krein-like formula for singular perturbations of self-adjoint operators and applications
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