Fluctuation properties of the Dirac spectrum at finite temperature and density

Abstract

The eigenvalue spectrum of the staggered Dirac matrix on a 6 3 × 4 lattice is analyzed in full QCD at finite temperature and in the presence of a chemical potential μ We construct the nearest-neighbor spacing distribution P( s) for the real eigenvalues (if μ = 0) and for the complex eigenvalues (if μ ≠ 0). At zero chemical potential, we find the expected agreement with the Wigner distribution of random matrix theory, both in the confinement phase and in the deconfinement phase. As μ is increased, we observe a crossover from Wigner statistics to Ginibre statistics, in accordance with random matrix predictions for complex non-hermitian matrices.