We calculate the shear η(T ) and bulk viscosities ζ (T ) as well as the electric conductivity σ e (T ) and heat conductivity κ(T ) within the Nambu-Jona-Lasinio model for three flavors as a function of temperature as well as the entropy density s(T ), pressure P(T ) and speed of sound c 2 s (T ). We compare the results with other models such as the Polyakov-Nambu-Jona-Lasinio (PNJL) model and the dynamical quasiparticle model (DQPM) and confront these results with lattice QCD data whenever available. We find the NJL model to have a limited predictive power for the thermodynamic variables and various transport coefficients above the critical temperature whereas the PNJL model and DQPM show acceptable results for the quantities of interest.

We study charm production in ultra-relativistic heavy-ion collisions by using the Parton-Hadron-String Dynamics (PHSD) transport approach. The initial charm quarks are produced by the Pythia event generator tuned to fit the transverse momentum spectrum and rapidity distribution of charm quarks from Fixed-Order Next-to-Leading Logarithm (FONLL) calculations. The produced charm quarks scatter in the quark-gluon plasma (QGP) with the off-shell partons whose masses and widths are given by the Dynamical Quasi-Particle Model (DQPM), which reproduces the lattice QCD equation-of-state in thermal equilibrium. The relevant cross sections are calculated in a consistent way by employing the effective propagators and couplings from the DQPM. Close to the critical energy density of the phase transition, the charm quarks are hadronized into D mesons through coalescence and fragmentation. The hadronized D mesons then interact with the various hadrons in the hadronic phase with cross sections calculated in an effective lagrangian approach with heavyquark spin symmetry. Finally, the nuclear modification factor RAA and the elliptic flow v2 of D 0 mesons from PHSD are compared with the experimental data from the STAR Collaboration for Au+Au collisions at √ sNN =200 GeV. We find that in the PHSD the energy loss of D mesons at high pT can be dominantly attributed to partonic scattering while the actual shape of RAA versus pT reflects the heavy-quark hadronization scenario, i.e. coalescence versus fragmentation. Also the hadronic rescattering is important for the RAA at low pT and enhances the D-meson elliptic flow v2.

We study charm production in Pb+Pb collisions at √ sNN =2.76 TeV in the Parton-Hadron-StringDynamics transport approach and the charm dynamics in the partonic and hadronic medium. The charm quarks are produced through initial binary nucleon-nucleon collisions by using the PYTHIA event generator taking into account the (anti-)shadowing incorporated in the EPS09 package. The produced charm quarks interact with off-shell massive partons in the quark-gluon plasma and are hadronized into D mesons through coalescence or fragmentation close to the critical energy density, and then interact with hadrons in the final hadronic stage with scattering cross sections calculated in an effective Lagrangian approach with heavy-quark spin symmetry. The PHSD results show a reasonable RAA and elliptic flow of D mesons in comparison to the experimental data for Pb+Pb collisions at √ sNN = 2.76 TeV from the ALICE Collaboration. We also study the effect of temperature-dependent off-shell charm quarks in relativistic heavy-ion collisions. We find that the scattering cross sections are only moderately affected by off-shell charm degrees of freedom. However, the position of the peak of RAA for D mesons depends on the strength of the scalar partonic forces which also have an impact on the D meson elliptic flow. The comparison with experimental data on the RAA suggests that the repulsive force is weaker for off-shell charm quarks as compared to that for light quarks. Furthermore, the effects from radiative charm energy loss appear to be low compared to the collisional energy loss up to transverse momenta of ∼ 15 GeV/c.