Quark Effects in the Gluon Condensate Contribution to the Scalar Glueball Correlation Function

One-loop quark contributions to the dimension-four gluon condensate term in the operator product expansion (OPE) of the scalar glueball correlation function are calculated in the MS-bar scheme in the chiral limit of $n_f$ quark flavours. The presence of quark effects is shown not to alter the cancellation of infrared (IR) singularities in the gluon condensate OPE coefficients. The dimension-four gluonic condensate term represents the leading power corrections to the scalar glueball correlator and, therein, the one-loop logarithmic contributions provide the most important condensate contribution to those QCD sum-rules independent of the low-energy theorem (the subtracted sum-rules).Comment: latex2e, 6 pages, 7 figures embedded in latex fil

Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant $d=4$ operator $F_{\mu\nu}^2(x)$ to all orders of perturbation theory in pure Yang-Mills gauge theory, whereby working in the Landau gauge. This renormalization is far from being trivial as mixing occurs with other $d=4$ gauge variant operators, which we identify explicitly. We determine the mixing matrix $Z$ to all orders in perturbation theory by using only algebraic arguments and consequently we can uncover a renormalization group invariant by using the anomalous dimension matrix $\Gamma$ derived from $Z$. We also present a future plan for calculating the mass of the lightest scalar glueball with the help of the framework we have set up.Comment: 17 page

Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential $s$ modulo the exterior spacetime derivative $d$ for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions $sa+db=0$ depending non trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition $sa+db=0$ besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms.Comment: 30 pages Latex file, ULB-TH-94/07, NIKHEF-H 94-1

Correlation induced phonon softening in low density coupled bilayer systems

We predict a possible phonon softening instability in strongly correlated coupled semiconductor bilayer systems. By studying the plasmon-phonon coupling in coupled bilayer structures, we find that the renormalized acoustic phonon frequency may be softened at a finite wave vector due to many-body local field corrections, particularly in low density systems where correlation effects are strong. We discuss experimental possibilities to search for this predicted phonon softening phenomenon.Comment: 4 pages with 2 figure

Rms-flux relation of Cyg X-1 with RXTE: dipping and nondipping cases

The rms (root mean square) variability is the parameter for understanding the emission temporal properties of X-ray binaries (XRBs) and active galactic nuclei (AGN). The rms-flux relation with Rossi X-ray Timing Explorer (RXTE) data for the dips and nondip of black hole Cyg X-1 has been investigated in this paper. Our results show that there exist the linear rms-flux relations in the frequency range 0.1-10 Hz for the dipping light curve. Moreover, this linear relation still remains during the nondip regime, but with the steeper slope than that of the dipping case in the low energy band. For the high energy band, the slopes of the dipping and nondipping cases are hardly constant within errors. The explanations of the results have been made by means of the ``Propagating Perturbation'' model of Lyubarskii (1997).Comment: 15 pages, 12 figures, Accepted for publication in Astrophysics & Space Scienc

Density Waves in Layered Systems with Fermionic Polar Molecules

A layered system of two-dimensional planes containing fermionic polar molecules can potentially realize a number of exotic quantum many-body states. Among the predictions, are density-wave instabilities driven by the anisotropic part of the dipole-dipole interaction in a single layer. However, in typical multilayer setups it is reasonable to expect that the onset and properties of a density-wave are modified by adjacent layers. Here we show that this is indeed the case. For multiple layers the critical strength for the density-wave instability decreases with the number of layers. The effect depends on density and is more pronounced in the low density regime. The lowest solution of the instability corresponds to the density waves in the different layers being in-phase, whereas higher solutions have one or several adjancet layers that are out of phase. The parameter regime needed to explore this instability is within reach of current experiments.Comment: 7 pages, 4 figures. Final version in EPJD, EuroQUAM special issue "Cold Quantum Matter - Achievements and Prospects

Persistent Spin Currents in Helimagnets

We demonstrate that weak external magnetic fields generate dissipationless spin currents in the ground state of systems with spiral magnetic order. Our conclusions are based on phenomenological considerations and on microscopic mean-field theory calculations for an illustrative toy model. We speculate on possible applications of this effect in spintronic devices.Comment: 9 pages, 6 figures, updated version as published, Journal referenc

Aging of a nanostructured Zn50Se50 alloy produced by mechanical alloying

The aging of a nanocrystalline equiatomic ZnSe alloy produced by mechanical alloying was investigated using X-ray diffraction (XRD) and differential scanning calorimetry (DSC) techniques. The measured XRD patterns showed that Se atoms located at interfacial component migrated with aging giving raise to a crystalline selenium (c-Se) phase. DSC spectra of heat-treated samples at temperatures above 221oC followed by quenching showed that the c-Se particles changed to the amorphous state. It was also observed that the as-milled and aged samples are highly hydrophilic. The lattice parameters and the average crystallite sizes were calculated as a function of time of aging and temperature of heat treatment.Comment: Submitted to Solid State Communications, 4 figure

Contraints on unified models for dark matter and dark energy using H(z)

The differential age data of astrophysical objects that have evolved passivelly during the history of the universe (e.g. red galaxies) allows to test theoretical cosmological models through the predicted Hubble function expressed in terms of the redshift $z$, $H(z)$. We use the observational data for $H(z)$ to test unified scenarios for dark matter and dark energy. Specifically, we focus our analysis on the Generalized Chaplygin Gas (GCG) and the viscous fluid (VF) models. For the GCG model, it is shown that the unified scenario for dark energy and dark matter requires some priors. For the VF model we obtain estimations for the free parameters that may be compared with further analysis mainly at perturbative level.Comment: Latex file, 10 pages, 19 figures in eps format. Accepted for publication in European Journal of Physics