Quark gap equation within the analytic approach to QCD

The compatibility between the QCD analytic invariant charge and chiral symmetry breaking is examined in detail. The coupling in question incorporates asymptotic freedom and infrared enhancement into a single expression, and contains only one adjustable parameter with dimension of mass. When inserted into the standard form of the quark gap-equation it gives rise to solutions displaying singular confining behavior at the origin. By relating these solutions to the pion decay constant, a rough estimate of about 880 MeV is obtained for the aforementioned mass-scale.Comment: Talk given by J.P. at 12th International QCD Conference (QCD05), 4 - 9 July 2005, Montpellier, France; 4 pages, 3 figure

DD-optimal saturated designs: a simulation study

In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric structure of the design and we compare them with the classical $D$-efficiency criterion. We perform a simulation study. In all the test cases we observe that designs with high values of $D$-efficiency have also high values of the new objective functions.Comment: 8 pages. Preliminary version submitted to the 7th IWS Proceeding

D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanations throughou

Numerical Study of the Ghost-Gluon Vertex in Landau gauge

We present a numerical study of the ghost-gluon vertex and of the corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau gauge for SU(2) lattice gauge theory. Data were obtained for three different lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta = 2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called smeared gauge fixing. We also consider two different sets of momenta (orbits) in order to check for possible effects due to the breaking of rotational symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a nonperturbative verification of the so-called nonrenormalization of the Landau ghost-gluon vertex. Finally, we use our data to evaluate the running coupling constant \alpha_s(p^2).Comment: 19 pages, 6 figures, 9 tables, using axodraw.sty; minor modifications in the abstract, introduction and conclusion

The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator Tr∫d4xFμν(D2)−1FμνTr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu} in the Landau gauge

We prove that the nonlocal gauge invariant mass dimension two operator $F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be consistently added to the Gribov-Zwanziger action, which implements the restriction of the path integral's domain of integration to the first Gribov region when the Landau gauge is considered. We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism. Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov-Taylor identity.Comment: 30 page

Spectral and Transport Properties of d-Wave Superconductors With Strong Impurities

One of the remarkable features of disordered d-wave superconductors is strong sensitivity of long range properties to the microscopic realization of the disorder potential. Particularly rich phenomenology is observed for the -- experimentally relevant -- case of dilute distributions of isolated impurity centers. Building on earlier diagrammatic analyses, the present paper derives and analyses a low energy effective field theory of this system. Specifically, the results of previous diagrammatic T-matrix approaches are extended into the perturbatively inaccessible low energy regimes, and the long range (thermal) transport behaviour of the system is discussed. It turns out that in the extreme case of a half-filled tight binding band and infinitely strong impurities (impurities at the unitary limit), the system is in a delocalized phase.Comment: 14 pages, two figures include

Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model

We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte

Optical symmetries and anisotropic transport in high-Tc superconductors

A simple symmetry analysis of in-plane and out-of-plane transport in a family of high temperature superconductors is presented. It is shown that generalized scaling relations exist between the low frequency electronic Raman response and the low frequency in-plane and out-of-plane conductivities in both the normal and superconducting states of the cuprates. Specifically, for both the normal and superconducting state, the temperature dependence of the low frequency $B_{1g}$ Raman slope scales with the $c-$axis conductivity, while the $B_{2g}$ Raman slope scales with the in-plane conductivity. Comparison with experiments in the normal state of Bi-2212 and Y-123 imply that the nodal transport is largely doping independent and metallic, while transport near the BZ axes is governed by a quantum critical point near doping $p\sim 0.22$ holes per CuO$_{2}$ plaquette. Important differences for La-214 are discussed. It is also shown that the $c-$ axis conductivity rise for $T\ll T_{c}$ is a consequence of partial conservation of in-plane momentum for out-of-plane transport.Comment: 16 pages, 8 Figures (3 pages added, new discussion on pseudogap and charge ordering in La214

Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). 31 pages, 12 figure