Electric conductivity is sensitive to effective cross sections among the particles of the partonic medium. We investigate the electric conductivity of a hot plasma of quarks and gluons, solving the relativistic Boltzmann equation. In order to extract this transport coefficient, we employ the Green-Kubo formalism and, independently, a method motivated by the classical definition of electric conductivity. To this end we evaluate the static electric diffusion current upon the influence of an electric field. Both methods give identical results. For the first time, we obtain numerically the Drude electric conductivity formula for an ultrarelativistic gas of quarks and gluons employing constant isotropic binary cross sections. Furthermore, we extract the electric conductivity for a system of massless quarks and gluons including screened binary and inelastic, radiative 2 ↔ 3 perturbative QCD scattering. Comparing with recent lattice results, we find an agreement in the temperature dependence of the conductivity.

We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify and point out the regime of validity of second-order fluid dynamics in relativistic shock phenomena. The transition from ideal to viscous shocks is demonstrated by varying the shear viscosity to entropy density ratio η/s. We also find that a good agreement between these two approaches requires a Knudsen number Kn < 1/2.

The shear viscosity of a gluon gas is calculated using the Green-Kubo relation. Time correlations of the energy-momentum tensor in thermal equilibrium are extracted from microscopic simulations using a parton cascade solving various Boltzmann collision processes. We find that the pQCD based gluon bremsstrahlung described by Gunion-Bertsch processes significantly lowers the shear viscosity by a factor of 3 − 8 compared to elastic scatterings. The shear viscosity scales with the coupling as η ∼ 1/(α 2 s log(1/α s )). For constant α s the shear viscosity to entropy density ratio η/s has no dependence on temperature. Replacing the pQCD-based collision angle distribution of binary scatterings by an isotropic form decreases the shear viscosity by a factor of 3.

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We solve the relativistic Riemann problem in viscous gluon matter employing a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio η/s from zero to infinity. We show that an η/s ratio larger than 0.2 prevents the development of well-defined shock waves on timescales typical for ultrarelativistic heavy-ion collisions. Comparisons with viscous hydrodynamic calculations confirm our findings.PACS numbers: 52.35.Tc, 24.10.Lx, 24.10.Nz In the 1970's, shock waves were theoretically predicted to occur in collisions of heavy nuclei [1]. This phenomenon has been experimentally investigated [2] and subsequently observed [3]. Recently, jet quenching [4] has been discovered in heavy-ion collisions at Brookhaven National Laboratory's Relativistic Heavy-Ion Collider (RHIC). In this context, very exciting jet-associated particle correlations [5] have been observed, which indicates the formation of shock waves in form of Mach cones [6] induced by supersonic partons moving through the quarkgluon plasma (QGP). If true, it could give a direct access to the equation of state of the QGP, because the Mach cone angle is given by α = arccos(c s /v jet ), where c s is the velocity of sound of the QGP. The velocity of sound is related to the equation of state via c 2 s = dP/de, where P is the pressure and e the energy density.Shock waves can form and propagate only if matter behaves like a fluid. The large measured elliptic flow coefficient v 2 [7] indicates that the QGP created at the RHIC could even be a nearly perfect fluid. This is confirmed by recent calculations within viscous hydrodynamics [8] and microscopic transport theory [9] which estimate the shear viscosity to entropy density ratio η/s to be less than 0.4 in order to not spoil the agreement with the v 2 data. However, it is an important question whether the η/s value deduced from v 2 data is sufficiently small to allow for the formation of shock waves.In this Letter we make an effort to answer this question by considering the relativistic Riemann problem in viscous gluon matter. Using the BAMPS microscopic transport model (BAMPS denotes the Boltzmann approach of multiparton scatterings) [10] we demonstrate the transition from ideal shock waves with zero width, to viscous shock waves with nonzero width, to free diffusion by varying the shear viscosity to entropy density ratio η/s from zero to infinity. We estimate the upper limit of the η/s ratio, for which shocks can still be observed experimentally on the time scale of an ultrarelativistic heavy-ion collision.The initial condition for the relativistic Riemann problem consists of two regions of thermodynamically equilibrated matter with different constant pressure separated by a membrane at z = 0, which is removed at t = 0. Matter is assumed to be homogeneous in the transverse At t = 0, the pressure is P0 = 5.43 GeVfm −3 for z < 0 and P4 = 2.22 GeVfm −3 for z > 0. The upper panel shows the pressure and the lower panel the veloc...