The gluon and ghost propagator and the influence of Gribov copies

The dependence of the Landau gauge gluon and ghost propagators on the choice of Gribov copies is studied in pure SU(3) lattice gauge theory. Whereas the influence on the gluon propagator is small, the ghost propagator becomes clearly affected by the copies in the infrared region. We compare our data with the infrared exponents predicted by the Dyson-Schwinger equation approachComment: Talk presented at Lattice2004(topology), Fermilab, June 21-26, 2004, 3 pages, 3 figure

Melt crystallization of ferroelectric copolymers of poly(vinylidene fluoride-trifluoroethylene)/

This dissertation is a study of the phase transition and melt crystallization of ferroelectric copolymers of poly(vinylidene fluoride-trifluoroethylene) (P(VDF-TrFE)) containing 83 mol% poly(vinylidene fluoride). The microstructure of crystallized P(VDF-TrFE) are characterized by vibrational spectroscopy to determine their chain conformation distribution, wide-angle X-ray diffraction (WAXD) to measure the crystal structure and determine the content of $\alpha$ and $\beta$ crystal phases. Differential scanning calorimetry (DSC) is used to measure the transition temperatures and their enthalpies. P(VDF-TrFE) is a polymorphic system exhibiting a Curie transition below its melting temperature, at which the copolymer undergoes a long range conformational change from a predominantly trans structure ($\beta$ phase) which can be ferroelectric, to a structure which has a mixture of trans and gauche conformations and is called the paraelectric $\alpha$ phase. Variable temperature FTIR studies have been made to follow the phase transition and to understand the multiple phase behavior that has been suggested for these copolymers. Factor analysis has been applied to the FTIR data to determine the number of crystal phases present for this copolymer composition. Melt crystallization under nonisothermal and isothermal conditions has been used to modify the structure of the copolymers and change both the Curie and melting temperatures. It is found that with slow cooling rates from the melt through the crystallization temperature, there is a stabilization of the paraelectric $\alpha$ phase which is then retained to different degrees on passing through the Curie transition on cooling. Under all crystallization conditions the copolymers exhibit two Curie transitions on cooling whose temperatures and intensities vary with cooling rate and crystallization time. The Curie temperature on cooling and subsequent heating is decreased upon slower cooling, reflecting an increase in the gauche chain conformers as evidenced by FT-Raman spectroscopy. WAXD data show that there are $\alpha$ and $\beta$ phase crystals present in samples that have been cooled slowly, accompanied by an increase in interplanar spacing which indicates that the $\beta$ phase also contains gauche defects. Longer isothermal crystallization at 135\sp\circC shows also that there is an increase in $\alpha$ phase content with longer crystallization time, though when crystallization is carried out at 135\sp\circC there is always a coexistence of $\alpha$ and $\beta$ phases in the final room temperature structure. Highly oriented P(VDF-TrFE) copolymers were prepared by solid-state coextrusion to aid in understanding the vibrational assignments in the copolymer. Infrared dichroism and WAXD were used to assess the sample orientation and measure the transition moment angles for some of the vibrations in the spectrum

Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum

In this talk we report on a recent lattice investigation of the Landau gauge gluon and ghost propagators in pure SU(3) lattice gauge theory with a special emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2 \le 0.3 \mathrm{GeV}^2$ we find the corresponding MOM scheme running coupling $\alpha_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of the ghost-gluon vertex function showing that it deviates only weakly from being constant. In addition we study the spectrum of low-lying eigenvalues and eigenfunctions of the Faddeev-Popov operator as well as the spectral representation of the ghost propagator.Comment: talk given by M. M.-P. at the Workshop on Computational Hadron Physics, Cyprus, September 200

Оценка уровня цифровой активности организаций розничной торговли России

The paper presents the main results of conjuncture monitoring which characterize the digital activity of retail trade organizations in 2018. The objects of observation are large, medium and small retail companies registered in Russia. The main goal of this work is to evaluate digital activity level of retail sector using the developed non-quantitative indicators that meet international standards and the country’s digital agenda. The presented set of harmonized indicators made it possible to identify the trends, scope and intensity of the spread of digital technologies in organizations. The level and intensity of digitalization are first determined on the basis of entrepreneurial opinions and intentions regarding the pace and scale of introducing digital technologies, readiness for digital transition, necessary skills to work with digital technologies, the use of specific digital products, as well as the main factors hindering digital transformation.В работе представлены основные результаты конъюнктурного обследования, характеризующие цифровую активность организаций розничной торговли в 2018 г. Объектами наблюдения были крупные, средние и малые предприятия розничной торговли, зарегистрированные в России. Основная цель данной работы заключалась в оценке уровня цифровой активности розничной торговли с помощью разработанных неколичественных индикаторов, соответствующих международным стандартам и цифровой повестке страны. Представленный набор гармонизированных показателей позволил выявить тенденции, масштаб и интенсивность распространения цифровых технологий в организациях. Уровень и интенсивность цифровизации впервые были определены на основе предпринимательских мнений и намерений относительно темпов и масштабов освоения цифровых технологий, готовности к цифровому переходу, сложившихся цифровых навыков, применения конкретных цифровых продуктов, а также основных факторов, препятствующих цифровой трансформации

Propagators in Coulomb gauge from SU(2) lattice gauge theory

A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is performed using large scale lattice simulations. The (equal-time) transverse gluon propagator, the ghost form factor d(p) and the Coulomb potential V_{coul} (p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator decreases like 1/p^{1+\eta} with \eta =0.5(1). At low momentum, the propagator is weakly momentum dependent. The small momentum behavior of the Coulomb potential is consistent with linear confinement. We find that the inequality \sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide evidence that the ghost form factor d(p) and f(p) acquire IR singularities, i.e., d(p) \propto 1/\sqrt{p} and f(p) \propto 1/p, respectively. It turns out that the combination g_0^2 d_0(p) of the bare gauge coupling g_0 and the bare ghost form factor d_0(p) is finite and therefore renormalization group invariant.Comment: 10 pages, 7 figure

Numerical Study of the Ghost-Gluon Vertex in Landau gauge

We present a numerical study of the ghost-gluon vertex and of the corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau gauge for SU(2) lattice gauge theory. Data were obtained for three different lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta = 2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called smeared gauge fixing. We also consider two different sets of momenta (orbits) in order to check for possible effects due to the breaking of rotational symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a nonperturbative verification of the so-called nonrenormalization of the Landau ghost-gluon vertex. Finally, we use our data to evaluate the running coupling constant \alpha_s(p^2).Comment: 19 pages, 6 figures, 9 tables, using axodraw.sty; minor modifications in the abstract, introduction and conclusion

Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared

We present recent results for the Landau-gauge gluon and ghost propagators in SU(3) lattice gluodynamics obtained on a sequence of lattices with linear extension ranging from L=64 to L=96 at $\beta = 5.70$, thus reaching "deep infrared" momenta down to 75 MeV. Our gauge-fixing procedure essentially uses a simulated annealing technique which allows us to reach gauge-functional values closer to the global maxima than standard approaches do. Our results are consistent with the so-called decoupling solutions found for Dyson-Schwinger and functional renormalization group equations.Comment: 6 pages, 5 figures. References added, minor changes to match published versio

Эффекты влияния экономико-технологического развития ИТ-сегмента на цифровую трансформацию розничной торговли

This paper presents the results of measuring intersectoral economic and technological effects, allowing to determine the degree of dependence between the segments that produce digital technologies and implement them. The basis for empirical calculations was the survey data of leaders among Russian IT companies and retail organizations on the current state of digital and business activity.The purpose of the work is to identify the presence and establish the strength of the relationship between these segments in terms of existing localized industry effects, expressed in the transfer of technology from the IT segment to retail. The authors of the work identified and tested several specific hypotheses, the general meaning of which was to suggest that retail trade in the current stage of economic development in Russia is susceptible to emerging trends in the rapidly changing IT services sector that can quickly and efficiently respond to the growth of the IT companies digital activity by increasing investments in digital technologies and increasing the intensity of their application in business processes.In particular, hypotheses were tested regarding the impact of business activity in the IT services segment on the growth of electronic commerce turnover, the use of online marketplaces, Big Data technologies, virtual and augmented reality technologies in retail trade organizations, as well as hypotheses suggesting a connection between the development of mobile applications in the IT segment and the use of mobile technologies, expectations regarding the growth of electronic goods turnover in retail organizations.The obtained results confirmed the majority of the hypotheses put forward, thereby supporting the authors’ general assumption about the existence of specific effects of the development of the IT segment on intersectoral technological transfers, revealed the existing specifics of penetration and spread of modern technological trends in trade, and also showed that the IT is currently important component in the process of digital transformation of Russian retail trade organizations.В статье ее авторами представлены результаты измерения межотраслевых экономико-технологических эффектов, позволяющих определить степень зависимости между макроэкономическими сегментами, продуцирующими цифровые технологии и внедряющими их. Цель работы - выявить наличие и установить силу связи между данными сегментами в части существующих локализованных отраслевых эффектов, выражающихся в переносе технологий из ИТ-сегмента в розничную торговлю. Основой для эмпирических расчетов выступили данные опросов руководителей российских ИТ-компаний и организаций розничной торговли о сложившемся состоянии цифровой и деловой активности.Авторами работы были обозначены и проверены несколько конкретных гипотез, общий смысл которых сводился к предположению, что розничная торговля в текущей фазе экономического развития в России действительно восприимчива к возникающим тенденциям в быстро изменяющемся секторе ИТ-услуг, способна оперативно и эффективно реагировать на рост цифровой активности ИТ-компаний увеличением инвестиций в цифровые технологии и повышением интенсивности их применения в бизнес-процессах. В частности, были выдвинуты и протестированы гипотезы, касающиеся влияния деловой активности в сегменте ИТ-услуг на прирост оборота электронной торговли, использование интернет-площадок, технологий Big Data, технологий виртуальной и дополненной реальности в организациях торговли, а также гипотезы, предполагающие наличие связи между разработкой мобильных приложений в ИТ-сегменте и использованием мобильных технологий, ожиданиями относительно роста электронного товарооборота в организациях розничной торговли.Полученные результаты дали доказательную базу для большинства выдвинутых гипотез, тем самым подтвердив теоретическое предположение авторов о существовании конкретных эффектов влияния развития ИТ-сегмента на межотраслевые технологические переносы, выявили существующую специфику проникновения и распространение актуальных технологических трендов в торговлю, а также показали, что ИТ-сегмент в настоящее время выступает важным составляющим в процессе цифровой трансформации российских розничных организаций

On practical problems to compute the ghost propagator in SU(2) lattice gauge theory

In SU(2) lattice pure gauge theory we study numerically the dependence of the ghost propagator G(p) on the choice of Gribov copies in Lorentz (or Landau) gauge. We find that the effect of Gribov copies is essential in the scaling window region, however, it tends to decrease with increasing beta. On the other hand, we find that at larger beta-values very strong fluctuations appear which can make problematic the calculation of the ghost propagator.Comment: 15 pages, 5 postscript figures. 2 Figures added Revised version as to be published in Phys.Rev.