Location of eigenvalues of three-dimensional non-self-adjoint Dirac operators

TL;DR

This paper establishes conditions under which the three-dimensional non-self-adjoint Dirac operator has no eigenvalues in certain complex regions, using smallness criteria on the potentials in Lebesgue spaces.

Contribution

It provides quantitative, easily checkable conditions for the absence of eigenvalues of non-Hermitian Dirac operators in unbounded complex regions.

Findings

Eigenvalues are absent in specified regions under small potential conditions

Conditions are quantitative and practically verifiable

Results extend understanding of spectral properties of non-self-adjoint Dirac operators

Abstract

We prove the absence of eigenvaues of the three-dimensional Dirac operator with non-Hermitian potentials in unbounded regions of the complex plane under smallness conditions on the potentials in Lebesgue spaces. Our sufficient conditions are quantitative and easily checkable.