Pablo Miranda: Eigenvalue Asymptotics for Dirichlet and Neumann Half-plane Magnetic Hamiltonians

In this talk we consider two Schrödinger operators with constant magnetic field on a half-plane, one defined with Dirichlet boundary conditions and another with Neumann boundary conditions. If V is a real, non-positive decaying electric potential, we study the discrete spectra of the original operators perturbed by V. In the Dirichlet case we show that, even under very weak perturbations V, infinitely many eigenvalues appear bellow the essential spectrum of the operator, while in the Newmann case that depends on the decaying rate of V. This is joint work with Vincent Bruneau and Georgi Raikov.