THOULESS ENERGY AND CORRELATIONS OF QCD DIRAC EIGENVALUES

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied f ar gauge field configurations given by a liquid of instantons. We find that for energy differences delta E below an energy scale E-c the eig envalue correlations are given by random matrix theories with the chir al symmetries of the QCD partition function. For eigenvalues near zero this energy scale shows a weak volume dependence that is not consiste nt with E-c similar to 1/L-2 which might be expected from the pion Com pton wavelength and from the behavior of the Thouless energy in mesosc opic systems. However, the numerical value of E-c for our largest volu mes is in rough agreement with estimates from the pion Compton wavelen gth. A scaling behavior consistent with E-c similar to 1/L-2 is found in the bulk of the spectrum. For delta E > E-c the number variance sho ws a linear dependence with a slope which is larger than the non-zero multifractality index of the wave functions. Finally, the average spec tral density and the scalar susceptibilities are discussed in the cont ext of quenched chiral perturbation theory. We argue that a non-zero v alue of the disconnected scalar susceptibility requires a linear depen dence of the number variance on delta E. (C) 1998 Elsevier Science B.V .