We calculate the shear viscosity over entropy density ratio η/s in Yang-Mills theory from the Kubo formula using an exact diagrammatic representation in terms of full propagators and vertices using gluon spectral functions as external input. We provide an analytic fit formula for the temperature dependence of η/s over the whole temperature range from a glueball resonance gas at low temperatures, to a high-temperature regime consistent with perturbative results. Subsequently we provide a first estimate for η/s in QCD.PACS numbers: 12.38. Aw, 11.10.Wx , 11.15.Tk Introduction -The experimental heavy-ion programs at RHIC [1,2] and at the LHC [3] explore the physics of the quark-gluon plasma (QGP). It turns out that the dynamics of the hot plasma created in heavy-ion collisions is well-described by hydrodynamics. Therefore, the determination of transport coefficients in the QGP is of great interest. One aspect is that the inference of the initial state physics requires a precise description of the hydrodynamical evolution, which in turn depends on transport coefficients as microscopic input, [4]. In particular, the viscosity over entropy ratio η/s governs the efficiency of the conversion of the initial spatial anisotropy into a momentum anisotropy of the final state.For the determination of η/s and its temperature dependence in the quark-gluon plasma, theoretical approaches face several challenges.The temperature regimes below and above the critical temperature T c are characterised by different degrees of freedom, and for temperatures T 2T c non-perturbative effects become important. Of particular interest is the vicinity of T c , where the minimum for η/s is expected [5,6]. A universal lower bound for η/s of 1/4π was conjectured in [7] using the AdS/CFT correspondence. Indeed, measurements of the elliptic flow v 2 indicate a value for η/s which is of the order of this lower bound [8]. The bound has been tested theoretically with several methods for the QGP [9-15], but also for other potentially perfect liquids, such as ultracold atoms [16][17][18].The Kubo formulae relate η to the energy-momentum tensor (EMT) [19]. Spectral functions are real-time quantities and cannot be obtained directly from Euclidean correlation functions. However, the direct calculation of real-time correlation functions represents a notoriously difficult problem in non-perturbative approaches to quantum field theory. Even though first computations in this direction have been performed e.g. in [20,21], we shall utilise Euclidean correlation functions within a numerical analytic continuation.In this work we study the shear viscosity over entropy ratio η/s in pure SU (3) Landau gauge Yang-Mills (YM) theory within the approach set-up in [9]. In the present

In this contribution a convenient synthetic method to obtain tetraacylgermanes Ge[C(O)R] (R=mesityl (1 a), phenyl (1 b)), a previously unknown class of highly efficient Ge-based photoinitiators, is described. Tetraacylgermanes are easily accessible via a one-pot synthetic protocol in >85 % yield, as confirmed by NMR spectroscopy, mass spectrometry, and X-ray crystallography. The efficiency of 1 a,b as photoinitiators is demonstrated in photobleaching (UV/Vis), time-resolved EPR (CIDEP), and NMR/CIDNP investigations as well as by photo-DSC studies. Remarkably, the tetraacylgermanes exceed the performance of currently known long-wavelength visible-light photoinitiators for free-radical polymerization.

We compute non-perturbative gluon spectral functions at finite temperature in quenched QCD with the maximum entropy method. We also provide a closed loop equation for the spectral function of the energy-momentum tensor in terms of the gluon spectral function.This setup is then used for computing the shear viscosity over entropy ratio η/s in a temperature range from about 0.4 Tc to 4.5 Tc. The ratio η/s has a minimum at about 1.25 Tc with the value of about 0.115. We also discuss extensions of the present results to QCD.PACS numbers: 12.38.Aw,11.10.Wx,11.15.Tk IntroductionHeavy-ion collisions at RHIC (Brookhaven) revealed about a decade ago, that the quark-gluon-plasma (QGP) is well-described by hydrodynamics [1]. It was also suggested that the QGP might be close to exhibit perfect fluidity signaled by a (almost) vanishing viscosity over entropy ratio η/s. Since then, many efforts have been made to increase the insight into the dynamics of the hot plasma, for a review see [2].The ratio η/s has been conjectured to satisfy a universal lower bound (KSS-bound) of 1/4π derived within the AdS-CFT correspondence [3]. Such a minimum can already be motivated within a quasi-particle picture: there, shear viscosity relates to a cross section, while the entropy density encodes the phase space volume of the quasi-particle. In the quasi-particle picture both quantities are related and their ratio is bounded from below.Measurements of the elliptic flow variable v 2 at RHIC and CERN indeed indicate a shear viscosity to entropy ratio for the QGP which is of the order of the AdS-CFT bound [4,5]. In turn, theoretical approaches to this quantity have to face the problem that perturbation theory is not applicable in the vicinity of the confinementdeconfinement transition temperature, and for a strongly correlated plasma.Transport coefficients can be obtained from the spectral function of the energy-momentum tensor via the Kubo relations [6]. However, most non-perturbative methods such as lattice QCD and functional continuum methods are so far limited to the computation of Euclidean correlation functions of the energy-momentum tensor, see e.g. [7][8][9][10] for lattice results. The related spectral function is then obtained via an integral equation. The latter has to be inverted from a discrete set of points, or more generally from numerical data, for example with the maximum entropy method (MEM), e.g.[11] or the Tikhonov regularization, e.g. [12]. So far, the resulting spectral functions ρ(ω, p) are subject to large statistical as well as systematical errors.In principle, MEM and similar inversion methods are powerful tools for providing reliable spectral functions, but this requires accurate initial Euclidean correlation

Electrochemical conversion of CO 2 to alcohols is one of the most challenging methods of conversion and storage of electrical energy in the form of high-energy fuels. The challenge lies in the catalyst design to enable its real-life implementation. Herein, we demonstrate the synthesis and characterization of a cobalt(III) triphenylphosphine corrole complex, which contains three polyethylene glycol residues attached at the meso -phenyl groups. Electron-donation and therefore reduction of the cobalt from cobalt(III) to cobalt(I) is accompanied by removal of the axial ligand, thus resulting in a square-planar cobalt(I) complex. The cobalt(I) as an electron-rich supernucleophilic d 8 -configurated metal centre, where two electrons occupy and fill up the antibonding d z 2 orbital. This orbital possesses high affinity towards electrophiles, allowing for such electronically configurated metals reactions with carbon dioxide. Herein, we report the potential dependent heterogeneous electroreduction of CO 2 to ethanol or methanol of an immobilized cobalt A 3 -corrole catalyst system. In moderately acidic aqueous medium (pH = 6.0), the cobalt corrole modified carbon paper electrode exhibits a Faradaic Efficiency (FE%) of 48 % towards ethanol production.