Classical and Quantum Chaos in Fundamental Field Theories

Details Classical and Quantum Chaos in Fundamental Field Theories Classical and Quantum Chaos in Fundamental Field Theories

2003-03-24

arxiv.org/abs/nlin/0303057v1

Nonlinear Sciences

Chaotic Dynamics

Contribution to the "Fourth International Conference on Dynamical Systems and Differential Equations" (Wilmington, North Carol

Scientific paper

An investigation of classical chaos and quantum chaos in gauge fields and fermion fields, respectively, is presented for (quantum) electrodynamics. We analyze the leading Lyapunov exponents of U(1) gauge field configurations on a $12^3$ lattice which are initialized by Monte Carlo simulations. We find that configurations in the strong coupling phase are substantially more chaotic than in the deconfinement phase. Considering the quantum case, complete eigenvalue spectra of the 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.

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