Universal Fluctuations in Spectra of the Lattice Dirac Operator.

Recently, Kalkreuter obtained the complete Dirac spectrum for an SU(2) lattice gauge theory. We performed a statistical analysis of his data and found that the eigenvalue correlations can be described by the Gaussian Symplectic Ensemble. Long range fluctuations are strongly suppressed: the variance of a sequence of levels containing n eigenvalues on average is given by 1 2π 2 (log n+const.). Our findings are in agreement with the anti-unitary symmetry of the lattice Dirac operator for N c = 2 with staggered fermions. For N c = 3 we predict that the eigenvalue correlations are given by the Gaussian Unitary Ensemble.