Asymptotics of the bound state induced by δ-interaction supported on a weakly deformed plane

DOI10.1063/1.5019931zbMath1380.81118arXiv1703.10854OpenAlexW2604879984MaRDI QIDQ3134137

Sylwia Kondej, Pavel Exner, Vladimir Lotoreichik

Publication date: 8 February 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.10854

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Operations with distributions and generalized functions (46F10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (7)

Spectral properties of the Dirac operator coupled with \(\delta\)-shell interactions ⋮ Singular Schrödinger operators and Robin billiards. Spectral properties and asymptotic expansions ⋮ Resonances for Laplacian perturbed on surface and cell membrane model ⋮ Leaky quantum structures ⋮ Scattering from local deformations of a semitransparent plane ⋮ On the eigenvalues of quantum graph Laplacians with large complex \(\delta\) couplings ⋮ Bound states asymptotics in the system with quantum wires in ℝ³

Cites Work

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• Upper bound for the number of bound states induced by the curvature of singular potential
• A spectral isoperimetric inequality for cones
• Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\)
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Schrödinger operators with singular interactions
• Curvature-induced bound states for a \(\delta\) interaction supported by a curve in \(\mathbb{R}^3\)
• Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces
• Quantum waveguides
• Geometrically induced spectrum in curved leaky wires
• Schrödinger operators withδ-interactions supported on conical surfaces
• Curvature-induced bound states in Robin waveguides and their asymptotical properties
• Discrete spectrum of interactions concentrated near conical surfaces
• On the bound states of Schrödinger operators with δ-interactions on conical surfaces
• Effective Hamiltonians for atoms in very strong magnetic fields
• Gap asymptotics in a weakly bent leaky quantum wire
• Hiatus perturbation for a singular Schrödinger operator with an interaction supported by a curve in R3
• Leaky Quantum Graphs: A Review
• On essential selfadjointness of the Weyl quantized relativistic Hamiltonian
• Bound states due to a strong   interaction supported by a curved surface
• Spectral analysis of photonic crystals made of thin rods
• On the spectrum of leaky surfaces with a potential bias
• Topologically nontrivial quantum layers
• Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model
• Approximation of Schrödinger operators with δ-interactions supported on hypersurfaces
• Variational proof of the existence of eigenvalues for star graphs
• On the existence of impurity bound excitons in one-dimensional systems with zero range interactions
• A Krein-like formula for singular perturbations of self-adjoint operators and applications

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