Magnetic bottles for the Neumann problem: the case of dimension 3

DOI10.1007/BF02829641zbMath1199.81016OpenAlexW1964781915MaRDI QIDQ1599741

Bernard Helffer, Arbderemane Mohamed

Publication date: 6 June 2002

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02829641

zbMATH Keywords

Schrödinger operatorsmagnetic fieldsspectral theorysuperconductivity

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Statistical mechanics of superconductors (82D55) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (17)

Energy of surface states for 3D magnetic Schrödinger operators ⋮ Semiclassical Spectral Asymptotics for a Two-Dimensional Magnetic Schrödinger Operator II: The Case of Degenerate Wells ⋮ Surface superconductivity in 3 dimensions ⋮ Spectral gaps for periodic Schrödinger operators with strong magnetic fields ⋮ Magnetic Laplacian in Sharp Three-dimensional Cones ⋮ Magnetic bottles for the Neumann problem: curvature effects in the case of dimension 3 (general case) ⋮ Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue ⋮ 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 ⋮ Remarks on the spectrum of the Neumann problem with magnetic field in the half-space ⋮ Reduced Landau-de Gennes functional and surface smectic state of liquid crystals ⋮ Local minimizers of the Ginzburg-Landau energy with magnetic field in three dimensions ⋮ Semiclassical 3D Neumann Laplacian with Variable Magnetic Field: A Toy Model ⋮ Bound states of a pair of particles on the half-line with a general interaction potential ⋮ The model magnetic Laplacian on wedges ⋮ Magnetic WKB constructions on surfaces ⋮ Plane waveguides with corners in the small angle limit

Cites Work

• Eigenvalues variation. I: Neumann problem for Sturm--Liouville operators
• Semi-classical analysis for the Schrödinger operator and applications
• Decay at infinity of eigenfunctions of Schrödinger operators with polynomial electro-magnetic field
• Stable nucleation for the Ginzburg-Landau system with an applied magnetic field
• Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity
• Surface nucleation of superconductivity in 3-dimensions
• Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells
• Multiple wells in the semi-classical limit I
• Modélisation du champ de retard à la condensation d'un supraconducteur par un problème de bifurcation
• Onset of superconductivity in decreasing fields for general domains
• Gauge Invariant Eigenvalue Problems in ℝⁿ and in ℝⁿ₊
• 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)
• Boundary concentration for eigenvalue problems related to the onset of superconductivity
• Magnetic bottles in connection with superconductivity
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