Strong diamagnetism for general domains and application

DOI10.5802/aif.2337zbMath1133.35073arXivmath-ph/0607071OpenAlexW1755328112MaRDI QIDQ2477564

Bernard Helffer, Søren Fournais

Publication date: 14 March 2008

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0607071

zbMATH Keywords

spectral theorysuperconductivityNeumann conditionbottom of the spectrum

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Statistical mechanics of superconductors (82D55)

Related Items (16)

On the transition to the normal phase for superconductors surrounded by normal conductors ⋮ The density of superconductivity in domains with corners ⋮ Geometric bounds for the magnetic Neumann eigenvalues in the plane ⋮ Non-monotonicity of the first eigenvalue for the 3D magnetic Robin Laplacian ⋮ Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential ⋮ Sums of magnetic eigenvalues are maximal on rotationally symmetric domains ⋮ The breakdown of superconductivity in the presence of magnetic steps ⋮ The Ginzburg-Landau functional with vanishing magnetic field ⋮ Thin domain limit and counterexamples to strong diamagnetism ⋮ Reduced Landau-de Gennes functional and surface smectic state of liquid crystals ⋮ Counterexample to strong diamagnetism for the magnetic Robin Laplacian ⋮ Lack of diamagnetism and the Little-Parks effect ⋮ Breakdown of superconductivity in a magnetic field with self-intersecting zero set ⋮ The Hardy inequality and the heat equation with magnetic field in any dimension ⋮ On the Ginzburg‐Landau critical field in three dimensions ⋮ The density of superconductivity in the bulk regime

Cites Work

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• 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
• Superconductivity near critical temperature
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• Magnetic bottles in connection with superconductivity

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