Quantum Chaos in Compact Lattice QED

Details Quantum Chaos in Compact Lattice QED Quantum Chaos in Compact Lattice QED

1998-12-10

arxiv.org/abs/hep-lat/9812010v1

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.

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