Seminario Fismat | Diomba Sambou (PUC)

Complex Eigenvalues for a Non-Self-Adjoint Dirac Operator

Abstract

We will consider a 2d Dirac operator with constant magnetic field perturbed by non-self-adjoint potentials. It is well known that when it is perturbed by certain self-adjoint potentials, then, there is creation and accumulation of real eigenvalues near every point of its essential spectrum given by a set of degenerate isolated eigenvalues called the Landau levels. Recently, similar results have been proved for Schrödinger operators perturbed by non-self-adjoint perturbations showing the existence of complex-valued potentials generating infinitely many non-real eigenvalues accumulating at every point of [0,+∞). We will present a similar result for the 2d Dirac operator above, showing the existence of non-self-adjoint perturbations generating infinitely many non-real eigenvalues accumulating at every Landau level.