On semiclassical eigenvalue distribution theorems for perturbations of the Landau problem

Carlos Villegas-Blas, UNAM, Mexico

Abstract

We study two different ways to consider the semiclassical limit of the eigenvalue distribution in clusters around the Landau levels associated to suitable perturbations of the Landau Hamiltonian. In the first one, we consider perturbations of the Landau problem keeping both the magnetic field strength and the value of the Planck's parameter fixed and then study the high energy asymptotics (joint work with A. Pushnitski and G . Raikov). We obtain that such distribution is determined by averages of the perturbation along straight lines on the motion plane. In the second one, we take both the magnetic field strength and the Planck's parameter depending on a parameter in such a way that the eigenvalue distribution is now determined by averages of the perturbation along classical orbits with fixed classical energy (joint work with G. Hernandez Dueñas, S. Perez-Esteva and A. Uribe).