Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a five percent change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.Comment: 2 pages, 2 figures, talk given by J.A.M. at the 30th International School of Nuclear Physics, Erice, Sicily from 16 - 24 September 200

What the Infrared Behaviour of QCD Vertex Functions in Landau gauge can tell us about Confinement

The infrared behaviour of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson-Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson-Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.Comment: 13 pages, 13 figures; to appear in the Proceedings of ``X Hadron Physics 2007'', Florianopolis, Brazil, March 26 - 31, 200

Dynamically induced scalar quark confinement

We employ a functional approach to investigate the confinement problem in quenched Landau gauge QCD. We demonstrate analytically that a linear rising potential between massive quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities is driven by the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken. We have thus uncovered a novel mechanism that directly links chiral symmetry breaking with confinement.Comment: 12 pages, 2 figures; v2: clarifications added and typos corrected, version to be published by MPL

Predicting the frequencies of diverse exo-planetary systems

Extrasolar planetary systems range from hot Jupiters out to icy comet belts more distant than Pluto. We explain this diversity in a model where the mass of solids in the primordial circumstellar disk dictates the outcome. The star retains measures of the initial heavy-element (metal) abundance that can be used to map solid masses onto outcomes, and the frequencies of all classes are correctly predicted. The differing dependences on metallicity for forming massive planets and low-mass cometary bodies are also explained. By extrapolation, around two-thirds of stars have enough solids to form Earth-like planets, and a high rate is supported by the first detections of low-mass exo-planets.Comment: 5 pages, 2 figures; accepted by MNRA

An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Testing of pear trees on their own roots in comparison with important used rootstocks under organic farming conditions with special regard to fire blight (E. amylovora)

Pear trees on their own roots are tested in comparison to grafted trees in growth and yield characteristics and with special regard to the tolerance to diseases, above all fire blight (Erwinia amylovora). In spring 2004 15 randomized trees of the cultivar 'Williams' from three variants (self rooted in vitro, self rooted long cuttings, grafted on Quince A) were planted in a pear orchard, which was heavily infected with fire blight (Erwinia amylovora) the previous years. The trees were left untreated. Growth and yield characteristics, plant diseases and tree losses were observed. After four years the in vitro self rooted trees were significantly more vigorous in growth than those grafted on quince A. The self rooted long cuttings were comparable in growth with grafts on quince, but showed high tree losses probably due to frost damages in the first winter one year after planting. However no infections with Erwinia amylovora could be observed so far. In a field trial with more cultivars and rootstock variants planted in 2006 at two organically managed sites more significant effects are expected in the next years

Real-Time Vector Automata

We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.Comment: 14 page

Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge

The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge parameter lambda equal to 1) and the minimal Coulomb gauge (corresponding to lambda = 0). For small values of lambda we find that the spatially-transverse gluon propagator D^tr(0,|\vec p|), considered as a function of the spatial momenta |\vec p|, is clearly infrared suppressed. This result is in agreement with the Gribov-Zwanziger scenario and with previous numerical results in the minimal Coulomb gauge. We also discuss the nature of the limit lambda -> 0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (lambda = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of lambda.Comment: 5 pages, 2 figures, one figure with additional results and extended discussion of some aspects of the results added and some minor clarifications. In v3: Various small changes and addition

Thermal Conductivity of Single Wall Carbon Nanotubes: Diameter and Annealing Dependence

The thermal conductivity, k(T), of bulk single-wall carbon nanotubes (SWNT's) displays a linear temperature dependence at low T that has been attributed to 1D quantization of phonons. To explore this issue further, we have measured the k(T) of samples with varying average tube diameters. We observe linear k(T) up to higher temperatures in samples with smaller diameters, in agreement with a quantization picture. In addition, we have examined the effect of annealing on k(T). We observe an enhancement in k(T) for annealed samples which we attribute to healing of defects and removal of impurities. These measurements demonstrate how the thermal properties of an SWNT material can be controlled by manipulating its intrinsic nanoscale properties.Comment: Proc. of the XV. Int. Winterschool on Electronic Properties of Novel Materials, Kirchberg/Tirol, Austria, 200