Vincent Bruneau: Spectral accumulation at the Landau levels

It is known that the so-called Landau Hamiltonian (i.e. the 2D Schrödinger operator with constant magnetic field) perturbed by an electric potential of definite sign have infinitely many eigenvalues near the Landau levels. The spectral structure of the 3D Schrödinger operator with constant magnetic field is more complicated because the Landau Levels are not isolated in the spectrum.

In this talk, we consider this 3D Schrödinger operator (with constant magnetic field) perturbed by an electric potential and study spectral accumulation phenomena. In particular we discuss the localization of the resonances (or eigenvalues) and asymptotic properties of the counting function of resonances near Landau Levels. With this aim of view, we prove an abstract result concerning the characteristic values of some holomorphic Fredholm families near an essential singularity. It is a joint work with J.F. Bony and G. Raikov.