Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra - art. no. 054501

Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in quantum chromodynamics (QCD). Importantly, RMT provides very efficient means to se parate different scales in the spectral fluctuations. We try to identify th e equivalent of a Thouless energy in complete spectra of the QCD Dirac oper ator for staggered fermions from SU(2) lattice gauge theory for different l attice size and gauge couplings. We focus on the bulk of the spectrum. In d isordered systems, the Thouless energy sets the universal scale for which R MT applies. This relates to recent theoretical studies which suggest a stro ng analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with h igh quality. We find deviations which allows us to give an estimate for thi s universal scale. Other deviations than these are seen whose possible orig in is discussed. Moreover, we work out higher order correlators as well, in particular three-point correlation functions. [S0556-2821(99)01901-3].