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 [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].

INVESTIGATION OF SPONTANEOUS CHIRAL-SYMMETRY BREAKING FROM LATTICE QCD WITH MASSLESS QUARKS

We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, zeros of the Bessel function and eigenvalue of Dirac operator is also given. The chiral condensate in this limit can be measured with small number of eigenvalues of the massless Dirac operator and without any ambiguous mass extrapolation. Results for lattice QCD with Kogut-Susskind quarks are shown.