Parton-hadron matter in- and out-off equilibrium

Abstract

We study the shear and bulk viscosities of partonic and hadronic matter – as well as the electric conductivity – as functions of temperature T within the Parton-Hadron-String Dynamics (PHSD) off-shell transport approach. Dynamical hadronic and partonic systems in equilibrium are studied by the PHSD simulations in a finite box with periodic boundary conditions. The ratio of the shear viscosity to entropy density η(T)/s(T) from PHSD shows a minimum (with a value of about 0.1) close to the critical temperature Tc, while it approaches the perturbative QCD (pQCD) limit at higher temperatures in line with lattice QCD results. For T < Tc, i.e. in the hadronic phase, the ratio η/s rises fast with decreasing temperature due to a lower interaction rate of the hadronic system and a significantly smaller number of degrees-of-freedom. The bulk viscosity ζ(T) – evaluated in the relaxation time approach – is found to strongly depend on the effects of mean fields (or potentials) in the partonic phase. We find a significant rise of the ratio ζ(T)/s(T) in the vicinity of the critical temperature Tc, when consistently including the scalar mean-field from PHSD, which is also in agreement with that from lQCD calculations. Furthermore, we present the results for the ratio (η + 3ζ/4)/s, which is found to depend non-trivially on temperature and to generally agree with the lQCD calculations as well. Within the PHSD calculations, the strong maximum of ζ(T)/η(T) close to Tc has to be attributed to mean-fields (or potential) effects that in PHSD are encoded in the temperature dependence of the quasiparticle masses, which is related to the infrared enhancement of the resummed (effective) coupling g(T). We also find that the dimensionless ratio of the electric conductivity over temperature σ0/T rises above Tc approximately linearly with T up to T = 2.5Tc, but approaches a constant above 5Tc, as expected qualitatively from perturbative QCD (pQCD).