Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra

Abstract

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 separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three--point correlation functions.

24 pages, 24 figures, all included except one figure, missing eps file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised version, to appear in PRD, minor modifications and corrected typos, Fig.4 revised

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• Random Matrix Theory and Chiral Symmetry in QCD
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• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD
• Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature
• Spectral ergodicity and normal modes in ensembles of sparse matrices
• Unfolding of the Spectrum for Chaotic and Mixed Systems
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Spectral correlations of the massive QCD Dirac operator at finite temperature
• Polyakov loops and spectral properties of the staggered Dirac operator
• Stochastic field theory for a Dirac particle propagating in gauge field disorder
• Handbook Article on Applications of Random Matrix Theory to QCD
• Color confinement, chiral symmetry breaking, and catalytic effect induced by monopole and instanton creations
• Semiclassical limits for the QCD Dirac operator
• Monopole and instanton effects in QCD
• Consecutive level spacings in the chiral Gaussian unitary ensemble: From the hard and soft edge to the bulk
• The zeros of the QCD partition function
• Long-ranged spectral correlations in eigenstate phases
• The Infrared Limit of the QCD Dirac Spectrum and Applications oc chiral Random Matrix Theory to QCD
• Transition to chaos in extended systems and their quantum impurity models
• Monopoles, spectra of overlap fermions, and eta-prime meson in external magnetic fields