Thoulesss energy and correlations of QCD dirac eigenvalues

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for an instanton liquid partition function. We find that for energy differences 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 perturbation 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 linear dependence. For the wave functions we find a small nonzero multifractality index. [S0031-9007(98)06623-X].