Dynamical chiral-symmetry breaking at T = 0 and T ≠ 0 in the Schwinger-Dyson equation with lattice QCD data

Dynamical chiral-symmetry breaking (DCSB) in QCD is investigated in the Schwinger-Dyson (SD) formalism based on lattice QCD data. From the quenched lattice data for the quark propagator in the Landau gauge, we extract the SD integral kernel function, the product of the quark-gluon vertex and the polarization factor in the gluon propagator, in an Ansatz-independent manner. We find that the SD kernel function exhibits the characteristic behavior of nonperturbative physics, such as infrared vanishing and strong enhancement at the intermediate-energy region around p 0.6GeV. The infrared and intermediate energy region (0.4GeV < p < 1.5GeV) is found to be most relevant for DCSB from analysis on the relation between the SD kernel and the quark mass function. We apply the lattice-QCD-based SD equation to thermal QCD, and calculate the quark mass function at the finite temperature. Spontaneously broken chiral symmetry is found to be restored at high temperature above 110 MeV.     

A brief remark on van der Waerden spaces

We demonstrate that Martin's axiom for -centered notions of forcing implies the existence of a van der Waerden space that is not a Hindman space. Our proof is an adaptation of the one given by M. Kojman and S. Shelah that such a space exists if one assumes the continuum hypothesis to be true.

     

Derivation of Magnetized-Wire Metrics in 5-Dimensional General Relativity

An infinite class of magnetized line-source (wire) metrics are here derived within the 5D GR (Kaluza-Klein) formalism. These metrics are cylindrically-symmetric (thus representing line-sources), and off-diagonal (thereby representing magnetized wire sources). The off-diagonality of these metrics is significant as all prior cylindrically-symmetric 5D GR metrics have been diagonal. In Kaluza-Klein theory, the vector potentials of EM are incorporated into the extended off-diagonal components of the metric. Thus, examination of such off-diagonal line source (magnetized wire) metrics is a hitherto untapped potential for 5D GR investigation.     

The Laguerre polyhedral decomposition: application to protein folds

An extension of the Voronoi tessellation, the Laguerre polyhedral decomposition, is introduced and applied to the analysis of the packing geometry of amino-acids in folded proteins. This method considers an ensemble of points with different weights and therefore it is well suited for a geometrical analysis of a set of objects with a wide size distribution. With this method it is shown that the true volumes occupied by the amino-acids inside a protein is better described than with the standard Voronoi procedure. This method allows defining unambiguously (without cut-off distance) the neighborhood for each amino-acid in a given protein and contact matrices can be established which contain all topological informations on the internal structure. Finally, a statistical analysis of the geometrical characteristics of the polyhedra attached to each amino-acid is done over a collection of 35 proteins. Received 20 November 2002 / Received in final form 26 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: sadoc@lps.u-psud.fr     

Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

From the recently determined structure of the delafossite YCuO_2.5, we argue that the Cu-O network has nearly independent Δ chains but with different interactions between the s = 1/2 spins. Motivated by this observation, we study the Δ chain for different ratios of the base-base and base-vertex interactions, J _bb/J _bv. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum is the same for total spins S _tot = 0 and 1, but not for S _tot = 2, and has a gap only in the interval 0.4874(1) ⩽ J _bb/J _bv ⩽ 1.53(1). The gap, known to be dispersionless for J _bb = J _bv, is found to acquire increasing k-dependence as J _bb/J _bv moves away from unity. Received 29 October 2002 / Received in final form 14 January 2003 Published online 6 March 2003 RID="a" ID="a"e-mail: sblundell@cea.fr RID="b" ID="b"e-mail: nunezreg@lps.u-psud.fr     

Cooling efficiency in collisions between Pd and He,Ne, Ar and Kr

The cooling of the metal cluster Pd₁₃ in an atmosphere of rare gas has been studied by means of computer simulation. By simulation, the average energy transfer in collisions between one cluster and one gas atom has been obtained. Emphasis has been placed on conditions when the temperatures of the colliding species are almost equal. All modes of motion, inclusive the translation, must be considered in order to obtain vanishing energy transfer at equilibrium. A simulation scheme is presented by which the energy transfer is zero to the cluster when the gas and the cluster temperatures are equal. At equilibrium the energy transfer does however not vanish for all impact parameters. In the collisions with Pd₁₃, the cluster is heated by collisions with a small impact parameter but equally cooled by collisions with a large impact parameter. Argon and krypton are found to cool Pd₁₃ equally efficiently while neon and helium are less efficient cooling agents. Received 28 September 2001 / Received in final form 8 August 2002 Published online 12 November 2002 RID="a" ID="a"e-mail: JanW@phc.gu.se     

Non-adiabatic transitions at a continuum edge

We consider interaction of a single level with a broad, tending to semi-infinite continuum. In an example of two exactly solvable problems, we show that for time dependent quantum systems the probability of the irreversible transition from a discrete level to a continuum is strongly inhibited or even completely suppressed by the presence of a discrete adiabatic level near the continuum edge. Received 10 October 2002 Published online 4 March 2003 RID="a" ID="a"e-mail: Alain.Sarfati@lac.u-psud.fr     

Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models

Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the nean square errors criterion,where the model matrix need not have full rank and the dispersion matrix can be singular.Our results show that any one of both estimates cannot be always superior to the other.Some sufficient criteria for any one of them to be better than the other are established.Some interesting relations between these two estimates are also given.     

General elephants of three-fold divisorial contractions

We treat three-fold divisorial contractions whose exceptional divisors contract to Gorenstein points. We prove that a general element in the anti-canonical system around the exceptional divisor has at worst Du Val singularities. As application to classification, we describe divisorial contractions to compound points, and moreover, we deduce that any divisorial contraction to a compound or point has discrepancy .

     

Serre's generalization of Nagao's theorem: An elementary approach

Let be a smooth projective curve over a field . For each closed point of let be the coordinate ring of the affine curve obtained by removing from . Serre has proved that is isomorphic to the fundamental group, , of a graph of groups , where is a tree with at most one non-terminal vertex. Moreover the subgroups of attached to the terminal vertices of are in one-one correspondence with the elements of , the ideal class group of . This extends an earlier result of Nagao for the simplest case .

Serre's proof is based on applying the theory of groups acting on trees to the quotient graph , where is the associated Bruhat-Tits building. To determine he makes extensive use of the theory of vector bundles (of rank 2) over . In this paper we determine using a more elementary approach which involves substantially less algebraic geometry.

The subgroups attached to the edges of are determined (in part) by a set of positive integers , say. In this paper we prove that is bounded, even when Cl is infinite. This leads, for example, to new free product decomposition results for certain principal congruence subgroups of , involving unipotent and elementary matrices.