Monopoles and Chaos

We decompose U(1) gauge fields into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. It turns out that there is a strong relation between the sizes of the monopole density and the Lyapunov exponent.Comment: Contribution to HEP-MAD'01 - High-Energy Physics International Conferences (Antananarivo, Madagascar, 2001/09/27 - 2001/10/05), 6 pages, 5 figure

Monopoles in Real Time for Classical U(1) Gauge Field Theory

U(1) gauge fields are decomposed into a monopole and photon part across the phase transition from the confinement to the Coulomb phase. We analyze the leading Lyapunov exponents of such gauge field configurations on the lattice which are initialized by quantum Monte Carlo simulations. We observe that the monopole field carries the same Lyapunov exponent as the original U(1) field. As a long awaited result, we show that monopoles are created and annihilated in pairs as a function of real time in excess to a fixed average monopole number.Comment: Contribution to the "International Conference on Color Confinement and Hadrons in Quantum Chromodynamics - Confinement 2003" (Tokyo, Japan, 2003-07-21 -- 2003-07-24); 5 pages; 6 figure

Quantum chaos in supersymmetric QCD at finite density

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory both in the confinement and in the deconfinement phase. This is indicative of quantum chaos. At nonzero chemical potential, the eigenvalues of the Dirac operator become complex and we discuss how $P(s)$ can be defined in the complex plane. Numerical results from an SU(2) simulation with staggered fermions in fundamental and adjoint representations are compared with predictions from non-hermitian random matrix theory, and agreement with the Ginibre ensemble is found for $\mu\approx 0.5$.Comment: Contribution to the Workshop on ``Finite Density QCD'' (Nara, Japan, 2003-07-10 -- 2003-07-12); 6 pages, 12 figure