Breaking a magnetic zero locus: asymptotic analysis

Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Semiclassical analysis; vanishing magnetic field; coherent states

Domaines: Equations aux dérivées partielles [math.AP]

Nicolas Raymond. Breaking a magnetic zero locus: asymptotic analysis. Mathematical Models and Methods in Applied Sciences, 2014, 24 (14), pp.2785-2817. ⟨10.1142/S0218202514500377⟩. ⟨hal-00790439v3⟩