Absence of eigenvalues for the generalized two-dimensional periodic Dirac operator

TL;DR

This paper proves that a generalized 2D periodic Dirac operator with certain matrix-valued potentials has no eigenvalues if the potential's bound relative to the free operator is zero, advancing spectral theory understanding.

Contribution

It establishes a spectral absence result for a broad class of 2D periodic Dirac operators with matrix-valued potentials, extending previous spectral analysis results.

Findings

No eigenvalues in the spectrum under zero relative bound condition

Spectral properties are characterized for generalized 2D periodic Dirac operators

Results apply to operators with complex matrix-valued potentials

Abstract

A generalized two-dimensional periodic Dirac operator is considered, with $L^{\infty}$-matrix-valued coefficients of the first order derivatives and with complex matrix-valued potential. It is proved that if the matrix-valued potential has zero bound relative to the free Dirac operator, then the spectrum of the operator in question contains no eigenvalues.