Diamagnetism versus Robin condition and concentration of ground states

A. Kachmar

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arXiv · 1507.08016

Diamagnetism versus Robin condition and concentration of ground states

A. Kachmar

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Abstract

We estimate the ground state energy for the magnetic Laplacian with a Robin condition. In a special asymptotic limit, we find that the magnetic field does not contribute to the two-term expansion of the ground state energy, thereby proving that the Robin condition weakens diamagnetism. We discuss a semi-classical version of the operator and prove that the ground states concentrate near the boundary points of maximal curvature.

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A. Kachmar. 2015-07-29. Diamagnetism versus Robin condition and concentration of ground states. https://arxiv.org/abs/1507.08016

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