Classical and quantum chaos in fundamental field theories. (English) Zbl 1174.81326
Summary: 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 \(\text{U}(1)\) gauge field configurations on a 123 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.
MSC:
81T80 | Simulation and numerical modelling (quantum field theory) (MSC2010) |
37N20 | Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) |
81Q50 | Quantum chaos |