Transport coefficients of hot and dense matter.

We present calculations for the shear viscosity of the hot and dense quark-gluon plasma (QGP) using the partonic scattering cross sections as a function of temperature $T$ and baryon chemical potential $\mu_B$ from the dynamical quasiparticle model (DQPM) that is matched to reproduce the equation of state of the partonic system above the deconfinement temperature $T_c$ from lattice QCD. To this aim we calculate the collisional widths for the partonic degrees of freedom at finite $T$ and $\mu_B$ in the time-like sector and conclude that the quasiparticle limit holds sufficiently well. Furthermore, the ratio of shear viscosity $\eta$ over entropy density $s$, i.e. $\eta/s$, is evaluated using these collisional widths and are compared to lQCD calculations for $\mu_B$ = 0 as well. We find that the ratio $\eta/s$ is in agreement with the results of calculations within the original DQPM on the basis of the Kubo formalism. Furthermore, there is only a very modest change of $\eta/s$ with the baryon chemical $\mu_B$ as a function of the scaled temperature $T/T_c(\mu_B)$.