Semiclassical Analysis with Vanishing Magnetic Fields

Nicolas Dombrowski (1) , Nicolas Raymond (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 IRMAR - Institut de Recherche Mathématique de Rennes

We analyze the 2D magnetic Laplacian in the semiclassical limit in the case when the magnetic field vanishes along a smooth curve. In particular, we prove local and micro-local estimates for the eigenfunctions and a complete asymptotic expansion of the eigenpairs.

Mots clés: Semiclassical limit; vanishing magnetic field; Agmon estimates; microlocal analysis

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Nicolas Dombrowski, Nicolas Raymond. Semiclassical Analysis with Vanishing Magnetic Fields. Journal of Spectral Theory, 2013, 3 (3), pp.423-464. ⟨10.4171/JST/50⟩. ⟨hal-00671999v5⟩