Semiclassical analysis with vanishing magnetic fields

DOI10.4171/JST/50zbMath1319.35127OpenAlexW1965605225MaRDI QIDQ361728

Nicolas Dombrowski, Nicolas Raymond

Publication date: 19 August 2013

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jst/50

zbMATH Keywords

semiclassical limitBorn-Oppenheimer approximationmicrolocal analysisAgmon estimatesasymptotic expansion of eigenvaluesmagnetic Laplacianvanishing magnetic field

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Variational methods for second-order elliptic equations (35J20)

Related Items (14)

Magnetic WKB constructions ⋮ Optimal magnetic Sobolev constants in the semiclassical limit ⋮ Breaking a magnetic zero locus: model operators and numerical approach ⋮ Breaking a magnetic zero locus: Asymptotic analysis ⋮ Decay of superconductivity away from the magnetic zero set ⋮ Magnetic effects in curved quantum waveguides ⋮ The breakdown of superconductivity in the presence of magnetic steps ⋮ Lack of diamagnetism and the Little-Parks effect ⋮ Eigenstates of the Neumann magnetic Laplacian with vanishing magnetic field ⋮ Semiclassical 3D Neumann Laplacian with Variable Magnetic Field: A Toy Model ⋮ A uniqueness theorem for higher order anharmonic oscillators ⋮ On the semiclassical Laplacian with magnetic field having self-intersecting zero set ⋮ Geometry and spectrum in 2D magnetic wells ⋮ Breakdown of superconductivity in a magnetic field with self-intersecting zero set

Cites Work

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• Discrete spectrum of a model Schrödinger operator on the half-plane with Neumann conditions
• Quantization of edge currents along magnetic barriers and magnetic guides
• Accurate eigenvalue asymptotics for the magnetic Neumann Laplacian
• Spectral asymptotics via the semiclassical Birkhoff normal form
• Stable nucleation for the Ginzburg-Landau system with an applied magnetic field
• Onset of superconductivity in decreasing fields for general domains
• Boundary concentration for eigenvalue problems related to the onset of superconductivity

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