Shear and bulk viscosities of strongly-interacting 'infinite'   parton-hadron matter within the parton-hadron-string transport approach
  We study the shear and bulk viscosities of partonic and hadronic matter 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 \eta(T)/s(T) from PHSD shows a minimum (with a value of about 0.1) close to the critical temperature T_c, while it approaches the perturbative QCD limit at higher temperatures in line with lattice QCD (lQCD) results. For T<T_c, i.e., in the hadronic phase, the ratio \eta/s rises fast with decreasing temperature due to a strong decrease of the entropy density $s$ in the hadronic phase at decreasing T. Within statistics, we obtain practically the same results in the Kubo formalism and in the relaxation time approximation. The bulk viscosity \zeta(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 \zeta(T)/s(T) in the vicinity of the critical temperature T_c, 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 (\eta+ 3\zeta/4)/s, which is found to depend nontrivially on temperature and to generally agree with the lQCD calculations as well. Within the PHSD calculations, the strong maximum of \zeta(T)/\eta(T) close to T_c has to be attributed to mean-field (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). 
V. Ozvenchuk, O. Linnyk, M. I. Gorenstein, E. L. Bratkovskaya, and W.   Cassing
hep-ph nucl-th