Semiclassical 3D Neumann Laplacian with Variable Magnetic Field: A Toy Model

DOI10.1080/03605302.2012.680558zbMath1254.35167OpenAlexW1963998253MaRDI QIDQ5200546

Nicolas Raymond

Publication date: 6 November 2012

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2012.680558

zbMATH Keywords

spectral theorysemiclassical analysisAgmon estimatesmagnetic Laplacian

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (3)

Magnetic WKB constructions ⋮ Geometry and spectrum in 2D magnetic wells ⋮ Magnetic Neumann Laplacian on a sharp cone

Cites Work

• Unnamed Item
• Semiclassical analysis with vanishing magnetic fields
• Discrete spectrum of a model Schrödinger operator on the half-plane with Neumann conditions
• Sharp asymptotics for the Neumann Laplacian with variable magnetic field: case of dimension 2
• Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian
• Spectral methods in surface superconductivity
• Spectral gaps for periodic Schrödinger operators with hypersurface magnetic wells: analysis near the bottom
• Semi-classical analysis for the Schrödinger operator and applications
• Stable nucleation for the Ginzburg-Landau system with an applied magnetic field
• Magnetic bottles for the Neumann problem: the case of dimension 3
• Surface nucleation of superconductivity in 3-dimensions
• Hearing the zero locus of a magnetic field
• Semiclassical analysis for the ground state energy of a Schrödinger operator with magnetic wells
• Schrödinger operators with non-degenerately vanishing magnetic fields in bounded domains
• Onset of superconductivity in decreasing fields for general domains
• Eigenvalue problems of Ginzburg–Landau operator in bounded domains
• Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schrödinger Operator.
• Boundary concentration for eigenvalue problems related to the onset of superconductivity
• Magnetic bottles in connection with superconductivity

This page was built for publication: Semiclassical 3D Neumann Laplacian with Variable Magnetic Field: A Toy Model