ON THE LOWEST ENERGY OF A 3D-MAGNETIC LAPLACIAN WITH AXISYMMETRICAL POTENTIAL

Nicolas Popoff (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study the bottom of the spectrum of a magnetic hamiltonian with axisymmetrical potential in R3. The associated magnetic field is planar, unitary and non-constant. The problem reduces to a 1D-family of singular Sturm-Liouville operators on the half-line. We study to associated band functions and we compare it to the "de Gennes" operators arising in the study of a 2D-hamiltonian with monodimensional, odd and discontinuous magnetic field. We show in particular that the lowest energy is higher in dimension 3.

Mots clés: Spectral theory; Magnetic Schrödinger operator; Linear eigenvalue problem

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]

Nicolas Popoff. ON THE LOWEST ENERGY OF A 3D-MAGNETIC LAPLACIAN WITH AXISYMMETRICAL POTENTIAL. 2013. ⟨hal-00803984v1⟩