Remarks on the spectrum of the Neumann problem with magnetic field in the half-space

DOI10.1063/1.1827922zbMath1076.82050OpenAlexW2016530280MaRDI QIDQ3024170

Françoise Truc, Arbderemane Mohamed

Publication date: 30 June 2005

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

Full work available at URL: https://doi.org/10.1063/1.1827922

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) General theory of partial differential operators (47F05) Statistical mechanics of superconductors (82D55) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (10)

Energy of surface states for 3D magnetic Schrödinger operators ⋮ Tunneling for the Robin Laplacian in smooth planar domains ⋮ On estimation of the number of eigenvalues of the magnetic Schrödinger operator in a three-dimensional layer ⋮ A 3D-Schrödinger operator under magnetic steps with semiclassical applications ⋮ Discrete spectrum of a model Schrödinger operator on the half-plane with Neumann conditions ⋮ The Schrödinger operator on an infinite wedge with a tangent magnetic field ⋮ Weyl formulae for the Robin Laplacian in the semiclassical limit ⋮ Bound states of a pair of particles on the half-line with a general interaction potential ⋮ Spectral asymptotics of the Dirichlet Laplacian in a conical layer ⋮ Plane waveguides with corners in the small angle limit

Cites Work

• Eigenvalues variation. I: Neumann problem for Sturm--Liouville operators
• Stable nucleation for the Ginzburg-Landau system with an applied magnetic field
• Magnetic bottles for the Neumann problem: the case of dimension 3
• Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity
• Surface nucleation of superconductivity in 3-dimensions
• ON AN ESTIMATE OF THE NUMBER OF POINTS OF THE NEGATIVE SPECTRUM OF THE SCHRÖDINGER OPERATOR
• Onset of superconductivity in decreasing fields for general domains
• Eigenvalue problems of Ginzburg–Landau operator in bounded domains
• Magnetic bottles for the Neumann problem: curvature effects in the case of dimension 3 (general case)
• Magnetic bottles in connection with superconductivity

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