Eigenvalues and eigenvectors of the staggered Dirac operator at finite temperature

We examine the eigenvalues and eigenvectors of the staggered Dirac operator on thermal ensembles created in QCD with two flavors of staggered quarks. We see that across the phase transition a gap opens in the spectrum. For finite volume lattices in the low-temperature phase the eigenvectors are extended, but generic field configurations in the high temperature phase give rise to localized eigenstates. We examine measures of the stability of such localization and find that at finite volumes localization occurs through Mott's mechanism of the formation of mobility edges. However, the band gap between the localized and extended states seem to scale to zero in the limit of large volume.