American Institute of Mathematical Sciences

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2003, 2003(Special): 596-603. doi: 10.3934/proc.2003.2003.596

Classical and quantum chaos in fundamental field theories

Harald Markum 1, and  Rainer Pullirsch 1,

1. 

Atominstitut der österreichischen Universitäten, Technische Universität Wien, Wiedner Haupstrabe 8-10, A-1040 Vienna, Austria, Austria

Received  September 2002 Published  April 2003

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: quantum chaos., classical chaos, Gauge theories.
Mathematics Subject Classification: Primary: 70H05, 81T2.
Citation: Harald Markum, Rainer Pullirsch. Classical and quantum chaos in fundamental field theories. Conference Publications, 2003, 2003 (Special) : 596-603. doi: 10.3934/proc.2003.2003.596
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