Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2000-07-07
Physics
High Energy Physics
High Energy Physics - Lattice
12 pages, 19 figures, talk presented at Confinement 2000 (Osaka, Japan, 2000-03-07 --2000-03-10)
Scientific paper
We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory on various lattice sizes. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor spacing distribution, $P(s)$. We further study two-color QCD at nonzero chemical potential, $\mu$, by constructing the spacing distribution of adjacent eigenvalues in the complex plane. We find that in all regions of their phase diagrams, compact lattice gauge theories have bulk spectral correlations given by random matrix theory, which is an indication for quantum chaos. In the confinement phase, the low-lying Dirac spectrum of these quantum field theories is well described by random matrix theory, exhibiting universal behavior.
Berg Bernd A.
Bittner Elmar
Lombardo Maria Paola
Markum Harald
Pullirsch Rainer
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