Strong diamagnetism for general domains and applications

Details Strong diamagnetism for general domains and applications Strong diamagnetism for general domains and applications

2006-07-31

arxiv.org/abs/math-ph/0607071v2

Physics

Mathematical Physics

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

Scientific paper

We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let $B$ be the strength of the magnetic field, and let $\lambda_1(B)$ be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that $B \mapsto \lambda_1(B)$ is monotone increasing for large $B$. Combined with the results of \cite{FournaisHelffer3}, this implies that all the `third' critical fields for strongly Type II superconductors coincide.

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