Using Grad's method, we calculate the entropy production and derive a formula for the second-order shear viscosity coefficient in a one-dimensionally expanding particle system, which can also be considered out of chemical equilibrium. For a one-dimensional expansion of gluon matter with Bjorken boost invariance, the shear tensor and the shear viscosity to entropy density ratio $η/s$ are numerically calculated by an iterative and self-consistent prescription within the second-order Israel-Stewart hydrodynamics and by a microscopic parton cascade transport theory. Compared with $η/s$ obtained using the Navier-Stokes approximation, the present result is about 20% larger at a QCD coupling $α_s \sim 0.3$(with $η/s\approx 0.18$) and is a factor of 2-3 larger at a small coupling $α_s \sim 0.01$. We demonstrate an agreement between the viscous hydrodynamic calculations and the microscopic transport results on $η/s$, except when employing a small $α_s$. On the other hand, we demonstrate that for such small $α_s$, the gluon system is far from kinetic and chemical equilibrium, which indicates the break down of second-order hydrodynamics because of the strong noneqilibrium evolution. In addition, for large $α_s$ ($0.3-0.6$), the Israel-Stewart hydrodynamics formally breaks down at large momentum $p_T\gtrsim 3$ GeV but is still a reasonably good approximation.
Shear viscosity is a dynamical property of fluid systems close to equilibrium, describing resistance to sheared flow. After reviewing the physics of viscosity and the reason it is usually difficult to compute, I discuss its importance within the theory of QCD and the obstacles to carrying out such a computation. A diagrammatic analysis requires extensive resummations and even then convergence is poor at physically relevant couplings. Lattice approaches require a poorly controlled analytical continuation of data from the Euclidean to the Minkowski domain. At present our best results for QCD she…
The leading-order weak-coupling shear viscosity of QCD was computed almost 20 years ago, and the extension to next-to-leading order is 4 years old. But these results have never been applied at finite baryon chemical potential $μ$, despite the fact that intermediate-energy heavy ion collisions and merging neutron stars may explore the Quark-Gluon Plasma in a regime where baryon chemical potentials are large. Here we extend the leading-log shear viscosity calculation to finite $μ$, and we argue that the convergence of the weak-coupling expansion, while questionable for achievable plasmas, should…
Influence of a temperature-dependent shear viscosity on the azimuthal asymmetries of transverse momentum spectra in ultrarelativistic heavy-ion collisions
We compute the shear viscosity of two-flavor QCD plasma in an external magnetic field in perturbative QCD at leading log order, assuming that the magnetic field is weak or soft: $eB\sim g^4\log(1/g)T^2$. We show that the shear viscosity takes a form $η=\barη(\bar B)T^3/(g^4\log(1/g))$ with a dimensionless function $\barη(\bar B)$ in terms of a dimensionless variable $\bar B=(eB)/(g^4\log(1/g)T^2)$. The variable $\bar B$ corresponds to the relative strength of the effect of cyclotron motions compared to the QCD collisions: $\bar B\sim l_{mfp}/l_{cyclo}$. We provide a full numerical result for t…
We have computed shear viscosity coefficient for hot and dense QCD matter within Polyakov loop extended quark meson(PQM) model for three flavors. Viscosity coefficient is estimated using Boltzmann equation within the relaxation time approximation. Relaxation times for quarks are calculated from elastic scattering of quarks and antiquarks via gluon exchange. Also the mean free paths of strange and light quarks are estimated for this cases. The calculations are performed at finite chemical potential. Thermodynamic properties like energy, pressure, entropy densities are also computed and compared…
The fireball concept of Rolf Hagedorn, developed in the 1960's, is an alternative description of hadronic matter. Using a recently derived mass spectrum, we use the transport model GiBUU to calculate the shear viscosity of a gas of such Hagedorn states, applying the Green-Kubo method to Monte-Carlo calculations. Since the entropy density is rising ad infinitum near $T_H$, this leads to a very low shear viscosity to entropy density ratio near $T_H$. Further, by comparing our results with analytic expressions, we find a nice extrapolation behavior, indicating that a gas of Hagedorn states comes …
We calculate for the first time the shear viscosity of ultrarelativistic Boson systems in the presence of a Bose-Einstein condensate (BEC). Two different methods are used. One is the Grad's method of moments and another is the Green-Kubo relation within a kinetic transport approach. In this work we consider a Boson system with isotropic elastic collisions and a gluon system with elastic scatterings described by perturbation QCD (pQCD). The results show that the presence of a BEC lowers the shear viscosity. This effect becomes stronger for the increasing proportion of the BEC in the Boson syste…
We calculate the transport coefficient of hadronic matter in the presence of temperature and magnetic field using the linear sigma model. In the relaxation time approximation, we estimate the shear viscosity over entropy density $η/s$. The point-like interaction rates of hadrons are evaluated through the $S$-matrix approach in the presence of a magnetic field to obtain the temperature and magnetic field-dependent relaxation time. We observe that the transport coefficients are anisotropic in the presence of the magnetic field. We calculate the temperature and magnetic field-dependent anisotropi…
We compute the shear viscosity of QCD with matter, including almost all next-to-leading order corrections -- that is, corrections suppressed by one power of $g$ relative to leading order. We argue that the still missing terms are small. The next-to-leading order corrections are large and bring $η/s$ down by more than a factor of 3 at physically relevant couplings. The perturbative expansion is problematic even at $T \simeq 100$ GeV. The largest next-to-leading order correction to $η/s$ arises from modifications to the qhat parameter, which determines the rate of transverse momentum diffusion. …
The chromo-electromagnetic field fluctuations in the quark-gluon plasma (QGP) play an important role as these field fluctuations result energy gain of heavy quarks. We consider these fluctuations and evaluate the transport coefficients, e.g., drag and diffusion coefficients of charm quarks and shear viscosity to entropy density ratio ($η/s$) of the QGP. We find a significant effect of such fluctuations on the transport coefficients. These fluctuations cause a reduction of the drag and diffusion coefficients. We also observe that the shear viscosity to entropy density ratio of the QGP is closer…
We investigate the shear viscosity $η$ of the classical Yang-Mills (CYM) field on a lattice by using the Green-Kubo formula, where the shear viscosity is calculated from the time-correlation function of the energy-momentum tensor in equilibrium. Dependence of the shear viscosity $η(g,T)$ on the coupling $g$ and temperature $T$ is represented by a scaling function $f_η(g^2T)$ as $η(g,T)=Tf_η(g^2T)$ due to the scaling-invariant property of the CYM. The explicit functional form of $f_η(g^2T)$ is successfully determined from the calculated shear viscosity: It turns out that $η(g,T)$ of the CYM fie…
The gravitational formfactor similar to shear viscosity is identified. In the time-like region it corresponds to the contribution of exotic hybrid meson. The exotic quantum numbers may be considered as a counterpart of dissipation in crossed channel. The ratio of viscosity to entropy density is estimated. The smallness due to holographic bound corresponds to the relative smallness of coupling of hybrid meson and the intrinsic transverse momentum, being the dynamical counterpart of temperature.
