A simple criterion for the existence of nonreal eigenvalues for a class of 2D and 3D Pauli operators

Abstract

In this work, we investigate the discrete spectrum generated by complex matrix-valued perturbations for a class of 2D and 3D Pauli operators with nonconstant magnetic fields. We establish a simple criterion for the potentials to produce discrete spectrum near the low ground energy of the operators. Moreover, in case of creation of nonreal eigenvalues, this criterion specifies also their location.