Shear and bulk viscosities of strongly interacting infinite parton-hadron matter within the parton-hadron-string dynamics 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).