Solving a Coupled Set of Truncated QCD Dyson-Schwinger Equations

Truncated Dyson-Schwinger equations represent finite subsets of the equations of motion for Green's functions. Solutions to these non-linear integral equations can account for non-perturbative correlations. A closed set of coupled Dyson-Schwinger equations for the propagators of gluons and ghosts in Landau gauge QCD is obtained by neglecting all contributions from irreducible 4-point correlations and by implementing the Slavnov-Taylor identities for the 3-point vertex functions. We solve this coupled set in an one-dimensional approximation which allows for an analytic infrared expansion necessary to obtain numerically stable results. This technique, which was also used in our previous solution of the gluon Dyson-Schwinger equation in the Mandelstam approximation, is here extended to solve the coupled set of integral equations for the propagators of gluons and ghosts simultaneously. In particular, the gluon propagator is shown to vanish for small spacelike momenta whereas the previoulsy neglected ghost propagator is found to be enhanced in the infrared. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, alpha_c approximately 9.5.Comment: 23 pages, 6 figures, LaTeX2

Quantum and Classical Ballistic Transport in Constricted Two-Dimensional Electron Gases

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Classical and Quantum Behavior in Mean-Field Glassy Systems

In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the dynamical instability found in mean-field spin glasses with a discontinuous transition. In mean-field models with pairwise interactions in a transverse field it is shown, in the framework of the static approximation, that such instability is suppressed at zero temperature.Comment: 9 Pages (including 5 Figures), Revtex, Proceedings of the XIV Sitges Conference, June 1996 (Barcelona) Spai

Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram

This review will be concerned with our knowledge of extended matter under the governance of strong interaction, in short: QCD matter. Strictly speaking, the hadrons are representing the first layer of extended QCD architecture. In fact we encounter the characteristic phenomena of confinement as distances grow to the scale of 1 fm (i.e. hadron size): loss of the chiral symmetry property of the elementary QCD Lagrangian via non-perturbative generation of "massive" quark and gluon condensates, that replace the bare QCD vacuum. However, given such first experiences of transition from short range perturbative QCD phenomena (jet physics etc.), toward extended, non perturbative QCD hadron structure, we shall proceed here to systems with dimensions far exceeding the force range: matter in the interior of heavy nuclei, or in neutron stars, and primordial matter in the cosmological era from electro-weak decoupling (10^-12 s) to hadron formation (0.5 10^-5 s). This primordial matter, prior to hadronization, should be deconfined in its QCD sector, forming a plasma (i.e. color conducting) state of quarks and gluons: the Quark Gluon Plasma (QGP).Comment: 146 pages, 83 figure

References

Acknowledgments We acknowledge useful discussions with Heiko Rieger, David Lancaster and Giorgio Parisi. J. J. Ruiz-Lorenzo is supported by an EC HMC(ERBFMBICT950429) grant. 10 Figure 4: D as a function of r for T = 0:45, L = 128. The line is our best fit to the behavior D(r) = c1P (r) + c2 by using data with 3 ^ r ^ 45. where errors have been evaluated by using the jack-knife method. The value of the residual O/2 (per degree of freedom) is very good, close to 0:2 (but since the data points are very correlated the number does not have necessarily a deep meaning). The agreement with the renormalization group prediction (see equation (21)) is very good. Our best numerical estimate for d\Lambda is ssc1=24

Magnetic Impurity in a Luttinger Liquid: A Conformal Field Theory Approach

We study the low-temperature properties of a spin- 1 2 magnetic impurity coupled to a one-dimensional interacting electron system. Using the newly developed formalism by Affleck and Ludwig, with a scale invariant boundary condition replacing the impurity, we exploit boundary conformal field theory to deduce the impurity thermal and magnetic response. In the case of only forward electron scattering off the impurity, we predict the same critical scaling as for the two-channel Kondo effect for non-interacting electrons, but with a novel Wilson ratio. Backward electron scattering off the impurity destabilizes this behavior and drives the system to a new fixed point. In the case of equal amplitudes for forward- and backward scattering (Kondo interaction) , we show that there are only two types of scaling behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a critical theory with an anomalous specific heat. The latter case agrees with a recent "poor-man-s..