From the Laplacian with variable magnetic field to the electric Laplacian in the semiclassical limit

Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We consider a twisted magnetic Laplacian with Neumann condition on a smooth and bounded domain of $\R^2$ in the semiclassical limit $h\to 0$. Under generic assumptions, we prove that the eigenvalues admit complete asymptotic expansions in powers of $h^{1/4}$.

Mots clés: Magnetic Laplacian; semiclassical analysis; spectral theory; Agmon estimates

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

Nicolas Raymond. From the Laplacian with variable magnetic field to the electric Laplacian in the semiclassical limit. Analysis & PDE, 2013, 6 (6), pp.1289-1326. ⟨10.2140/apde.2013.6.1289⟩. ⟨hal-00625260v4⟩