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Register a new userSpectral representation of the shear viscosity for local scalar QFTs at finite temperature
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In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard K{a}ll{e}n-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $eta_{0}$. As an example, we calculate $eta_{0}$ in $phi^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.
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The microscopic formulas for the shear viscosity $eta$, the bulk viscosity $zeta$, and the corresponding relaxation times $tau_pi$ and $tau_Pi$ of causal dissipative relativistic fluid-dynamics are obtained at finite temperature and chemical potential by using the projection operator method. The non-triviality of the finite chemical potential calculation is attributed to the arbitrariness of the operator definition for the bulk viscous pressure.We show that, when the operator definition for the bulk viscous pressure $Pi$ is appropriately chosen, the leading-order result of the ratio, $zeta$ over $tau_Pi$, coincides with the same ratio obtained at vanishing chemical potential. We further discuss the physical meaning of the time-convolutionless (TCL) approximation to the memory function, which is adopted to derive the main formulas. We show that the TCL approximation violates the time reversal symmetry appropriately and leads results consistent with the quantum master equation obtained by van Hove. Furthermore, this approximation can reproduce an exact relation for transport coefficients obtained by using the f-sum rule derived by Kadanoff and Martin. Our approach can reproduce also the result in Baier et al.(2008) Ref. cite{con} by taking into account the next-order correction to the TCL approximation, although this correction causes several problems.
This work reports on investigations of the effects on the evolution of viscous hydrodynamics and on the flow coefficients of thermal dileptons, originating from a temperature-dependent specific shear viscosity $eta/s (T)$ at temperatures beyond 180 MeV formed at the Relativistic Heavy-Ion Collider (RHIC). We show that the elliptic flow of thermal dileptons can resolve the magnitude of $eta/s$ at the high temperatures, where partonic degrees of freedom become relevant, whereas discriminating between different specific functional forms will likely not be possible at RHIC using this observable.
In this paper we study the shear viscosity temperature dependence of $SU(3)$--gluodynamics within lattice simulation. To do so, we measure the correlation functions of energy-momentum tensor in the range of temperatures $T/T_cin [0.9, 1.5]$. To extract the values of shear viscosity we used two approaches. The first one is to fit the lattice data with some physically motivated ansatz for the spectral function with unknown parameters and then determine shear viscosity. The second approach is to apply the Backus-Gilbert method which allows to extract shear viscosity from the lattice data nonparametrically. The results obtained within both approaches agree with each other. Our results allow us to conclude that within the temperature range $T/T_c in [0.9, 1.5]$ SU(3)--gluodynamics reveals the properties of a strongly interacting system, which cannot be described perturbatively, and has the ratio $eta/s$ close to the value ${1}/{4pi}$ in $N = 4$ Supersymmetric Yang-Mills theory.
We explore the influence of a temperature-dependent shear viscosity over entropy density ratio $eta/s$ on the azimuthal anisotropies v_2 and v_4 of hadrons at various rapidities. We find that in Au+Au collisions at full RHIC energy, $sqrt{s_{NN}}=200$ GeV, the flow anisotropies are dominated by hadronic viscosity at all rapidities, whereas in Pb+Pb collisions at the LHC energy, $sqrt{s_{NN}}=2760$ GeV, the flow coefficients are affected by the viscosity both in the plasma and hadronic phases at midrapidity, but the further away from midrapidity, the more dominant the hadronic viscosity is. We find that the centrality and rapidity dependence of the elliptic and quadrangular flows can help to distinguish different parametrizations of $(eta/s)(T)$. We also find that at midrapidity the flow harmonics are almost independent of the decoupling criterion, but show some sensitivity to the criterion at back- and forward rapidities.
We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nt=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a^2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nt=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV
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