Workshop Nosevol #3

Vincent Bruneau : Counting function of the eigenvalues for perturbations of magnetic Schrödinger operators.

We consider several magnetic Schrödinger operators whose spectra have a band structure : constant magnetic field on the plan or on the half-plane with Dirichlet (resp., Neumann) boundary conditions and magnetic field created by an infinite rectilinear wire bearing a constant courant (in $\R^3$). Then we study the distribution of the eigenvalues below the infima of the essential spectra for perturbation by a non negative potential V. We show how the behavior of the band functions and of the associated eigenfunctions are combined with the potential properties to analyse the counting function of the eigenvalues near the infima of the essential spectra. Joint work with P. Miranda and G. Raikov and with N. Popoff.