Anomalous scaling of passive scalar in turbulence and in equilibrium

We analyze multi-point correlation functions of a tracer in an incompressible flow at scales far exceeding the scale $L$ at which fluctuations are generated (quasi-equilibrium domain) and compare them with the correlation functions at scales smaller than $L$ (turbulence domain). We demonstrate that the scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales

Scaling studies of QCD with the dynamical HISQ action

We study the lattice spacing dependence, or scaling, of physical quantities using the highly improved staggered quark (HISQ) action introduced by the HPQCD/UKQCD collaboration, comparing our results to similar simulations with the asqtad fermion action. Results are based on calculations with lattice spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical HISQ quarks. The strange and charm quark masses are near their physical values, and the light-quark mass is set to 0.2 times the strange-quark mass. We look at the lattice spacing dependence of hadron masses, pseudoscalar meson decay constants, and the topological susceptibility. In addition to the commonly used determination of the lattice spacing through the static quark potential, we examine a determination proposed by the HPQCD collaboration that uses the decay constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the lattice artifacts in the HISQ simulations are much smaller than those in the asqtad simulations at the same lattice spacings and quark masses.Comment: 36 pages, 11 figures, revised version to be published. Revisions include discussion of autocorrelations and several clarification

Nonlocal Scalar Quantum Field Theory: Functional Integration, Basis Functions Representation and Strong Coupling Expansion

Nonlocal QFT of one-component scalar field $\varphi$ in $D$-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions $\mathcal{Z}$ as a functional of external source $j$, coupling constant $g$, and spatial measure $d\mu$ is studied. An expression for GF $\mathcal{Z}$ in terms of the abstract integral over the primary field $\varphi$ is given. An expression for GF $\mathcal{Z}$ in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator $\hat{L}$ over the separable HS basis. The classification of functional integration measures $\mathcal{D}\left[\varphi\right]$ is formulated, according to which trivial and two nontrivial versions of GF $\mathcal{Z}$ are obtained. Nontrivial versions of GF $\mathcal{Z}$ are expressed in terms of $1$-norm and $0$-norm, respectively. The definition of the $0$-norm generator $\varPsi$ is suggested. Simple cases of sharp and smooth generators are considered. Expressions for GF $\mathcal{Z}$ in terms of integrals over the separable HS with new integrands are obtained. For polynomial theories $\varphi^{2n},\, n=2,3,4,\ldots,$ and for the nonpolynomial theory $\sinh^{4}\varphi$, integrals over the separable HS in terms of a power series over the inverse coupling constant $1/\sqrt{g}$ for both norms ($1$-norm and $0$-norm) are calculated. Critical values of model parameters when a phase transition occurs are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated. A comparison of two GFs $\mathcal{Z}$, one in the case of uncountable HS integral and one obtained using the Parseval-Plancherel identity, is given.Comment: 26 pages, 2 figures; v2: significant additions in the text; prepared for the special issue "QCD and Hadron Structure" of the journal Particles; v3: minimal corrections; v4: paragraphs added related to Reviewer comment

Approximate Killing Vectors on S^2

We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically S^2. When solutions of Killing's equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes.Comment: 4 pages, 3 figures, submitted to Physical Review D, revtex

S\mathcal{S}-Matrix of Nonlocal Scalar Quantum Field Theory in the Representation of Basis Functions

Nonlocal quantum theory of one-component scalar field in $D$-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$-matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant $g$ in the form of an infrared smooth function of argument $x$ for space without boundary. Nonlocality is given by evolution of Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter $l$. By representation of the $\mathcal{S}$-matrix in terms of abstract functional integral over primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. And, by expression of $\mathcal{S}$-matrix in terms of the partition function, the representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for discrete case where basis functions are Hermite functions, and for continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$-matrix are investigated within the framework of variational principle based on Jensen inequality. Equations with separable kernels satisfied by variational function $q$ are found and solved, yielding results for both the polynomial theory $\varphi^{4}$ and the nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$-matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are illustrated numerically. For simplicity of numerical calculation: the $D=1$ case is considered, and propagator for the free theory $G$ is in the form of Gaussian function typically in the Virton-Quark model. The formulation for nonlocal QFT in momentum $k$ space of extra dimensions with subsequent compactification into physical spacetime is discussed.Comment: 38 pages, 18 figures; v2: significant text editing; v3: text and plots edited, references and acknowledgments added; prepared for the special issue of the journal Particles in memory of G.V. Efimo

Predictions for Polarized-Beam/Vector-Polarized-Target Observables in Elastic Compton Scattering on the Deuteron

Motivated by developments at HIGS at TUNL that include increased photon flux and the ability to circularly polarize photons, we calculate several beam-polarization/target-spin dependent observables for elastic Compton scattering on the deuteron. This is done at energies of the order of the pion mass within the framework of Heavy Baryon Chiral Perturbation Theory. Our calculation is complete to O(Q^3) and at this order there are no free parameters. Consequently, the results reported here are predictions of the theory. We discuss paths that may lead to the extraction of neutron polarizabilities. We find that the photon/beam polarization asymmetry is not a good observable for the purpose of extracting \alpha_n and \beta_n. However, one of the double polarization asymmetries, \Sigma_x, shows appreciable sensitivity to \gamma_{1n} and could be instrumental in pinning down the neutron spin polarizabilities.Comment: 26 pages, 13 figures, revised version to be published in PR

A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

On the number of Mather measures of Lagrangian systems

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest

IRIS: A new generation of IRAS maps

The Infrared Astronomical Satellite (IRAS) had a tremendous impact on many areas of modern astrophysics. In particular it revealed the ubiquity of infrared cirrus that are a spectacular manifestation of the interstellar medium complexity but also an important foreground for observational cosmology. With the forthcoming Planck satellite there is a need for all-sky complementary data sets with arcminute resolution that can bring informations on specific foreground emissions that contaminate the Cosmic Microwave Background radiation. With its 4 arcmin resolution matching perfectly the high-frequency bands of Planck, IRAS is a natural data set to study the variations of dust properties at all scales. But the latest version of the images delivered by the IRAS team (the ISSA plates) suffer from calibration, zero level and striping problems that can preclude its use, especially at 12 and 25 micron. In this paper we present how we proceeded to solve each of these problems and enhance significantly the general quality of the ISSA plates in the four bands (12, 25, 60 and 100 micron). This new generation of IRAS images, called IRIS, benefits from a better zodiacal light subtraction, from a calibration and zero level compatible with DIRBE, and from a better destriping. At 100 micron the IRIS product is also a significant improvement from the Schlegel et al. (1998) maps. IRIS keeps the full ISSA resolution, it includes well calibrated point sources and the diffuse emission calibration at scales smaller than 1 degree was corrected for the variation of the IRAS detector responsivity with scale and brightness. The uncertainty on the IRIS calibration and zero level are dominated by the uncertainty on the DIRBE calibration and on the accuracy of the zodiacal light model.Comment: 16 pages, 17 figures, accepted for publication in ApJ (Suppl). Higher resolution version available at http://www.cita.utoronto.ca/~mamd/IRIS/IrisTechnical.htm