THOULESSS ENERGY AND CORRELATIONS OF QCD DIRAC EIGENVALUES

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied f or an instanton liquid partition function. We find that for energy dif ferences delta E below an energy scale E-c, identified as the Thouless energy, the eigenvalue correlations are given by random matrix theory . The value of E-c shows a weak volume dependence for eigenvalues near zero and is consistent with a scaling of E-c similar to 1/L-2 in the bulk of the spectrum in agreement with estimates from chiral perturbat ion theory that E-c/Delta approximate to (FpiL2)-L-2/pi (with average level spacing Delta). For gamma E > E-c the number variance shows a li near dependence. For the wave functions we find a small nonzero multif ractality index. [S0031-9007(98)06623-X].