Equivalent of a Thouless energy in lattice QCD Dirac spectra

Abstract

Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD). In mesoscopic physics, the Thouless energy sets the universal scale for which RMT applies. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator with staggered fermions and $S{U}_c(2)$ lattice gauge fields. Comparing lattice data with RMT predictions we find deviations which allow us to give an estimate for this scale.

Comments: LATTICE99 (theor. devel.), 3 pages, 4 figures