Shear and bulk viscosities of strongly interacting “infinite” parton-hadron matter within the parton-hadron-string dynamics transport approach

Abstract

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 $\ensuremath{\eta}(T)/s(T)$ 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 $\ensuremath{\eta}/s$ 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 $\ensuremath{\zeta}(T)$---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 $\ensuremath{\zeta}(T)/s(T)$ 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 $(\ensuremath{\eta}+3\ensuremath{\zeta}/4)/s$, 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 $\ensuremath{\zeta}(T)/\ensuremath{\eta}(T)$ 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 $g(T)$.