When the 3D magnetic Laplacian meets a curved edge in the semiclassical limit

Nicolas Popoff (1) , Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study the magnetic Laplacian in the case when the Neumann boundary contains an edge. We provide complete asymptotic expansions in powers of $h^{1/4}$ of the low lying eigenpairs in the semiclassical limit $h\to 0$. In order to get our main result we establish a general method based on a normal form procedure, microlocal arguments, the Feshbach-Grushin reduction and the Born-Oppenheimer approximation.

Mots clés: Magnetic Laplacian; Semiclassical analysis; Singular domain; Normal form

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

Nicolas Popoff, Nicolas Raymond. When the 3D magnetic Laplacian meets a curved edge in the semiclassical limit. SIAM Journal on Mathematical Analysis, 2013, 45 (4), pp.2354-2395. ⟨10.1137/130906003⟩. ⟨hal-00746862v2⟩