Quantum Chaos in Compact Lattice QED

Abstract

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.

11 pages, 4 figures

References in corpus (2)

• Evidence for quantum chaos in the plasma phase of QCD
• Chaotic behavior of confining lattice gauge field configurations

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• Exact Zero-Modes of the Compact QED Dirac Operator
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• Low-lying Dirac eigenmodes and monopoles in 4D compact QED
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• Supersymmetry and Integrability in Planar Mechanical Systems