Stochastic field evolution of disoriented chiral condensates

I present a summary of recent work \cite{BRS} where we describe the time-evolution of a region of disoriented chiral condensate via Langevin field equations for the linear $\sigma$ model. We analyze the model in equilibrium, paying attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a ultraviolet cutoff independent theory that reproduces quantitatively the expected equilibrium behavior of pion and $\sigma$ quantum fields. We also estimate the viscosity $\eta(T)$, which controls the dynamical timescale in the Langevin equation, so that the near equilibrium dynamical response agrees with theoretical expectations.Comment: 3 pages, 3 figures, contribution to the proceedings of Lattice0

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

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

Langevin Evolution of Disoriented Chiral Condensate

As the matter produced in a relativistic heavy ion collision cools through the QCD phase transition, the dynamical evolution of the chiral condensate will be driven out of thermal equilibrium. As a prelude to analyzing this evolution, and in particular as a prelude to learning how rapid the cooling must be in order for significant deviations from equilibrium to develop, we present a detailed analysis of the time-evolution of an idealized region of disoriented chiral condensate. We set up a Langevin field equation which can describe the evolution of these (or more realistic) linear sigma model configurations in contact with a heat bath representing the presence of other shorter wavelength degrees of freedom. We first analyze the model in equilibrium, paying particular attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use known results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a theory which is ultraviolet cutoff independent and that reproduces quantitatively the expected equilibrium behavior of the quantum field theory of pions and sigma fields over a wide range of temperatures. Finally, we estimate the viscosity $\eta(T)$, which controls the dynamical timescale in the Langevin equation, by requiring that the timescale for DCC decay agrees with previous calculations. The resulting $\eta(T)$ is larger than that found perturbatively. We also determine the temperature below which the classical field Langevin equation ceases to be a good model for the quantum field dynamics.Comment: 19 pages, 7 figures, uses RevTex; v2 very small change to the caption of Fig.7. Version to appear in Nucl. phys.

A Kinetic Analysis of Footfall Patterns at Landing in Netball: A Follow-up Study

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Improved Determination of the Mass of the 1−+1^{-+} Light Hybrid Meson From QCD Sum Rules

We calculate the next-to-leading order (NLO) $\alpha_s$-corrections to the contributions of the condensates $$ and $^2$ in the current-current correlator of the hybrid current g\barq(x)\gamma_{\nu}iF_{\mu\nu}^aT^aq(x) using the external field method in Feynman gauge. After incorporating these NLO contributions into the Laplace sum-rules, the mass of the $J^{PC}$=$1^{-+}$ light hybrid meson is recalculated using the QCD sum rule approach. We find that the sum rules exhibit enhanced stability when the NLO $\alpha_s$-corrections are included in the sum rule analysis, resulting in a $1^{-+}$ light hybrid meson mass of approximately 1.6 GeV.Comment: revtex4, 10 pages, 7 eps figures embedded in manuscrip

Thin-Film Metamaterials called Sculptured Thin Films

Morphology and performance are conjointed attributes of metamaterials, of which sculptured thin films (STFs) are examples. STFs are assemblies of nanowires that can be fabricated from many different materials, typically via physical vapor deposition onto rotating substrates. The curvilinear--nanowire morphology of STFs is determined by the substrate motions during fabrication. The optical properties, especially, can be tailored by varying the morphology of STFs. In many cases prototype devices have been fabricated for various optical, thermal, chemical, and biological applications.Comment: to be published in Proc. ICTP School on Metamaterials (Augsut 2009, Sibiu, Romania

Resummation of the hadronic tau decay width with the modified Borel transform method

A modified Borel transform of the Adler function is used to resum the hadronic tau decay width ratio. In contrast to the ordinary Borel transform, the integrand of the Borel integral is renormalization--scale invariant. We use an ansatz which explicitly accounts for the structure of the leading infrared renormalon. Further, we use judiciously chosen conformal transformations for the Borel variable, in order to map sufficiently away from the origin the other ultraviolet and infrared renormalon singularities. In addition, we apply Pade approximants for the corresponding truncated perturbation series of the modified Borel transform, in order to further accelerate the convergence. Comparing the results with the presently available experimental data on the tau hadronic decay width ratio, we obtain $\alpha_s(M^z) = 0.1192 +- 0.0007_{exp.} +- 0.0010_{EW+CKM} +- 0.0009_{th.} +- 0.0003_{evol.}$. These predictions virtually agree with those of our previous resummations where we used ordinary Borel transforms instead.Comment: 32 pages, 2 eps-figures, revtex; minor changes in the formulations; a typo in Eq.(47) corrected; version as appearing in Phys. Rev.

Current correlators to all orders in the quark masses

The contributions to the coefficient functions of the quark and the mixed quark-gluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short- and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms of non-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.Comment: 24 pages, LateX file, TUM-T31-21/92, 1 postscript file include

Photoionisation loading of large Sr+ ion clouds with ultrafast pulses

This paper reports on photoionisation loading based on ultrafast pulses of singly-ionised strontium ions in a linear Paul trap. We take advantage of an autoionising resonance of Sr neutral atoms to form Sr+ by two-photon absorption of femtosecond pulses at a wavelength of 431nm. We compare this technique to electron-bombardment ionisation and observe several advantages of photoionisation. It actually allows the loading of a pure Sr+ ion cloud in a low radio-frequency voltage amplitude regime. In these conditions up to 4x10^4 laser-cooled Sr+ ions were trapped