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arXiv · 1309.5320

Ground Energy of the Magnetic Laplacian in Polyhedral Bodies

Virginie Bonnaillie-Noël·Monique Dauge·Nicolas Popoff
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Abstract

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the model problems (continuity, semi-continuity, existence of generalized eigenfunctions). We prove estimates for the remainders of our asymptotic formula. Lower bounds are obtained with the help of a classical IMS partition based on adequate coverings of the polyhedral domain, whereas upper bounds are established by a novel construction of quasimodes, qualified as sitting or sliding according to spectral properties of local model problems.

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Virginie Bonnaillie-Noël, Monique Dauge, Nicolas Popoff. 2013-12-04. Ground Energy of the Magnetic Laplacian in Polyhedral Bodies. https://arxiv.org/abs/1309.5320

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