TY - JOUR
T1 - Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
AU - Guhr, T.
AU - Ma, J. Z.
AU - Meyer, S.
AU - Wilke, T.
PY - 1999
Y1 - 1999
N2 - 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. We focus on the bulk of the spectrum. 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.
AB - 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. We focus on the bulk of the spectrum. 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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U2 - 10.1103/PhysRevD.59.054501
DO - 10.1103/PhysRevD.59.054501
M3 - Article
AN - SCOPUS:16644395409
SN - 1550-7998
VL - 59
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 5
ER -