Absence of correlations in the QCD Dirac spectrum at high temperature

Details Absence of correlations in the QCD Dirac spectrum at high temperature Absence of correlations in the QCD Dirac spectrum at high temperature

2009-06-29

arxiv.org/abs/0906.5373v2

Phys.Rev.Lett.104:031601,2010

Physics

High Energy Physics

High Energy Physics - Lattice

4 pages, some rewording for clarification; references added

Scientific paper

10.1103/PhysRevLett.104.031601

I propose a simple model of the distribution of the small eigenvalues of the QCD Dirac operator well above the finite temperature phase transition where chiral symmetry is restored and the spectral density at zero vanishes. Assuming the absence of correlations between different regions of the low lying spectrum I derive analytic formulas for the distribution of the first two eigenvalues. I find good agreement with data obtained using the overlap Dirac operator in quenched SU(2) lattice simulations. This suggests that if chiral symmetry is restored spectral correlations are not important and all the statistical properties of the spectrum are encoded in the spectral density.

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