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Classical and quantum chaos in fundamental field theories

Pages: 596 - 603, Issue Special, July 2003

 Abstract        Full Text (206.6K)              

Harald Markum - Atominstitut der österreichischen Universitäten, Technische Universität Wien, Wiedner Haupstrabe 8-10, A-1040 Vienna, Austria (email)
Rainer Pullirsch - Atominstitut der österreichischen Universitäten, Technische Universität Wien, Wiedner Haupstrabe 8-10, A-1040 Vienna, Austria (email)

Abstract: 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.

Keywords:  Gauge theories, classical chaos, quantum chaos.
Mathematics Subject Classification:  Primary: 70H05, 81T25.

Received: September 2002; Published: April 2003.