Strong diamagnetism for general domains and applications

2006/07/31 by S. Fournais, Søren Fournais, Bernard Helffer +3 · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.math-ph/0607071

A few typos corrected. One argument given in more details. Version to be published in AIF

openalex publication_date 2006/07/31 · arxiv created 2007/02/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let B be the strength of the magnetic field, and let λ₁(B) be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that B ↦ λ₁(B) is monotone increasing for large B. Combined with the results of \citeFournaisHelffer3, this implies that all the `third' critical fields for strongly Type II superconductors coincide.

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