Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1998-12-10
Phys.Rev. D59 (1999) 097504
Physics
High Energy Physics
High Energy Physics - Lattice
11 pages, 4 figures
Scientific paper
10.1103/PhysRevD.59.097504
Complete eigenvalue spectra of the staggered Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator.
Berg Bernd A.
Markum Harald
Pullirsch Rainer
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