Sharp exponential decay for solutions of the stationary perturbed Dirac equation

We determine the largest rate of exponential decay at infinity for non-trivial solutions to the Dirac equation nψ + ψ = 0in Rn, being n the massless Dirac operator in dimension n ≥ 2 and a (possibly non-Hermitian) matrix-valued perturbation such that |(x)|∼|x|-at infinity, for-∞ < < 1. Also, we show that our results are sharp for n {2, 3}, 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 ≤ 0 and n {2, 3}.