Dirac eigenvalues and eigenvectors at finite temperature

We investigate the eigenvalues and eigenvectors of the staggered Dirac oper ator in the vicinity of the chiral phase transition of quenched SU(3) latti ce gauge theory. We consider both the global features of the spectrum and t he local correlations. In the chirally symmetric phase, the local correlati ons in the bulk of the spectrum are still described by random matrix theory , and we investigate the dependence of the bulk Thouless energy on the simu lation parameters. At and above the critical point, the properties of the l ow-lying Dirac eigenvalues depend on the Z(3)-phase of the Polyakov loop. I n the real phase, they are no longer described by chiral random matrix theo ry. We also investigate the localization properties of the Dirac eigenvecto rs in the different Z(3)-phases.