Thouless 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 δE below an energy scale E_c, identified as the Thouless energy, the eigenvalue correlations are given by random matrix theory. The value of E_cshows a weak volume dependence for eigenvalues near zero and is consistent with a scaling of E_c∼1/L² in the bulk of the spectrum in agreement with estimates from chiral perturbation theory that E_c/Δ≈F_π²L²/π(with average level spacingδ)ForδE >E_cthe number variance shows a linear dependence. For the wave functions we find a small nonzero multifractality index.