Breaking a magnetic zero locus: asymptotic analysis
Résumé
This paper deals with the spectral analysis of the Laplacian in presence of a magnetic field vanishing along a broken line. Denoting by $\theta$ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when $\theta$ goes to $0$. The investigation deeply uses a coherent states decomposition and a microlocal analysis of the eigenfunctions.
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