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

TL;DR

This paper provides a straightforward criterion to determine when complex perturbations of 2D and 3D Pauli operators with nonconstant magnetic fields generate nonreal eigenvalues near the ground energy, including their locations.

Contribution

It introduces a simple, practical criterion for the existence and location of nonreal eigenvalues in the spectrum of perturbed Pauli operators with complex potentials.

Findings

Criterion for discrete spectrum near ground energy

Location of nonreal eigenvalues specified

Applicable to 2D and 3D Pauli operators with nonconstant magnetic fields

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.