Towards the Equation of State of Classical SU(2) Lattice Gauge Theory

We determine numerically the full complex Lyapunov spectrum of SU(2) Yang-Mills fields on a 3-dimensional lattice from the classical chaotic dynamics. The equation of state, S(E), is determined from the Kolmogorov-Sinai entropy extrapolated to the large size limit.Comment: 12 pages, 8 PS figures, LaTe

Explicit analysis of the lateral mechanics of web spans

All previous analyses of webs being steered through process equipment have required enforcement of assumed boundary conditions. An example is the normal entry boundary condition which has been employed in many web/roller analyses.Explicit finite element analyses show much promise for studying all types of web handling problems. The primary benefit of this type of analysis is that only very basic assumptions are required, average web velocity and tension for example. Beyond this the interaction of webs with rollers are governed entirely by forces of contact and friction that develop between the web and rollers. Conditions of stick and slip are possible. Additional benefits include the ability to study web deformations and stresses which may result in the development of boundary conditions that can be employed in models that are computationally less expensive.This paper will focus on a study of the lateral behavior of a web transiting a set of rollers in a process machine, one of which will be misaligned. The misalignment will be increased until there is interaction with an upstream span, a phenomena that has been previously called moment interaction. Any steering of a web laterally in a process machine produces reactions that must be resolved as frictional forces between the web and rollers. Thus the slightest misalignment of a roller will induce some slippage between the web and an upstream roller. That slippage will become gross as the degree of misalignment increases until it migrates around the upstream roller and induces lateral deformation in the upstream span. These phenomena will be studied and results will be compared to experiments. Finally an assessment of potential boundary conditions will be made.Mechanical and Aerospace Engineerin

Quantum Chaos in Compact Lattice QED

Complete eigenvalue spectra of the staggered 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. Combining this with previous results on QCD, we conjecture that quite generally the non-linear couplings of quantum field theories lead to a chaotic behavior of the eigenvalues of the Dirac operator.Comment: 11 pages, 4 figure

Ising spins coupled to a four-dimensional discrete Regge skeleton

Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model employed in this work limits the choice of the link lengths to a finite number. To get more precise insight into the behavior of the four-dimensional discrete Regge model, we coupled spins to the fluctuating manifolds. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field theory of the Ising model on a static four-dimensional lattice.Comment: 19 pages, 7 figure

An Extension of the Fractional Parentage Expansion to Nonrelativistic and Relativistic SU(3)fSU(3)_{f} Dibaryon Calculations

The fractional parentage expansion method is extended from $SU(2)_{f}$ nonrelativistic to $SU(3)_{f}$ and relativistic dibaryon calculations. A transformation table between physical bases and symmetry bases for the $SU(3)_{f}$ dibaryon is provided. A program package has been written for dibaryon calculation based on the fractional parentage expansion method.Comment: 15 pages text plus 18 pages tables, latex, no figure

Microscopic correlations of non-Hermitian Dirac operators in three-dimensional QCD

In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using a random matrix model approach. Our results apply to non-Hermitian Dirac operators in three-dimensional QCD with broken flavor symmetry and in four-dimensional QCD in the bulk of the spectrum. The derivation follows earlier results of Fyodorov, Khoruzhenko and Sommers for complex spectra exploiting the existence of orthogonal polynomials in the complex plane. Explicit analytic expressions are given for all microscopic k-point correlation functions in the presence of an arbitrary even number of massive quarks, both in the limit of strong and weak non-Hermiticity. In the latter case the parameter governing the non-Hermiticity of the Dirac matrices is identified with the influence of the chemical potential

Random matrices beyond the Cartan classification

It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in practical calculations of physical observables. In this paper we show that a large number of non-hermitean random matrix ensembles defined by physically motivated symmetries - chiral symmetry, time reversal invariance, space rotation invariance, particle-hole symmetry, or different reality conditions - can likewise be identified with symmetric spaces. We give explicit representations of the random matrix ensembles identified with lateral algebra subspaces, and of the corresponding symmetric subalgebras spanning the group of invariance. Among the ensembles listed we identify as special cases all the hermitean ensembles identified with Cartan classes of symmetric spaces and the three Ginibre ensembles with complex eigenvalues.Comment: 41 pages, no figures. References and comments added; the representation of ensemble 15 changed to quaternion real. Version accepted for publication on J. Phys.

Monopole Clustering and Color Confinement in the Multi-Instanton System

We study color confinement properties of the multi-instanton system, which seems to carry an essence of the nonperturbative QCD vacuum. Here we assume that the multi-instanton system is characterized by the infrared suppression of instantons as $f(\rho)\sim \rho^{-5}$ for large size $\rho$. We first investigate a monopole-clustering appearing in the maximally abelian (MA) gauge by considering the correspondence between instantons and monopoles. In order to clarify the infrared monopole properties, we make the ``block-spin'' transformation for monopole currents. The feature of monopole trajectories changes drastically with the instanton density. At a high instanton density, there appears one very long and highly complicated monopole loop covering the entire physical vacuum. Such a global network of long-monopole loops resembles the lattice QCD result in the MA gauge. Second, we observe that the SU(2) Wilson loop obeys an area law and the static quark potential is approximately proportional to the distance $R$ between quark and anti-quark in the multi-instanton system using the SU(2) lattice with a total volume of $V=(10 fm)^4$ and a lattice spacing of $a=0.05 fm$. We extract the string tension from the $5 \times 10^{6}$ measurements of Wilson loops. With an instanton density of $(N/V)=(1/fm)^4$ and a average instanton size of $\bar{\rho}=0.4 fm$, the multi-instanton system provides the string tension of about $0.4 GeV/fm$