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

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

1998-06-02

arxiv.org/abs/hep-lat/9806003v2

Phys.Rev. D59 (1999) 054501

Physics

High Energy Physics

High Energy Physics - Lattice

24 pages, 24 figures, all included except one figure, missing eps file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.ep

Scientific paper

10.1103/PhysRevD.59.054501

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 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.

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