Sharp exponential decay for solutions of the stationary perturbed Dirac equation

Abstract

We determine the largest rate of exponential decay at infinity for non-trivial solutions to the Dirac equation [Formula: see text] being [Formula: see text] the massless Dirac operator in dimension [Formula: see text] and [Formula: see text] a (possibly non-Hermitian) matrix-valued perturbation such that [Formula: see text] at infinity, for [Formula: see text]. Also, we show that our results are sharp for [Formula: see text], providing explicit examples of solutions that have the prescripted decay, in presence of a potential with the related behavior at infinity. As a consequence, we investigate the exponential decay at infinity for the eigenfunctions of the perturbed massive Dirac operator, and determine the sharpest possible decay in the case that [Formula: see text] and [Formula: see text].