The formation of Mach cones is studied in a full $(3+1)$-dimensional setup of ultrarelativistic heavy-ion collisions, considering a transverse and longitudinal expanding medium at Relativistic Heavy-Ion Collider energies. For smooth initial condition
s and central collisions the jet-medium interaction is investigated using high-energy jets and various values of the ratio of shear viscosity over entropy density, $eta/s$. For small viscosities, the formation of Mach cones is proven, whereas for larger viscosities the characteristic structures smear out and vanish eventually. The formation of a double-peak structure both in a single- and in a multiple-jet event is discussed.
Using a microscopic transport model we investigate the evolution of conical structures originating from the supersonic projectile moving through the hot matter of ultrarelativistic particles. Using different scenarios for the interaction between proj
ectile and matter, and different transport properties of the matter, we study the formation and structure of Mach cones. Especially, a dependence of the Mach cone angle on the details and rate of the energy deposition from projectile to the matter is investigated. Furthermore, the two-particle correlations extracted from the numerical calculations are compared to an analytical approximation. We find that the propagation of a high energetic particle through the matter does not lead to the appearance of a double peak structure as observed in the ultrarelativistic heavy-ion collision experiments. The reason is the strongly forward-peaked energy and momentum deposition in the head shock region. In addition, by adjusting the cross section we investigate the influence of the viscosity to the structure of Mach cones. A clear and unavoidable smearing of the profile depending on a finite ratio of shear viscosity to entropy density is clearly visible.
Fast thermalization and a strong build up of elliptic flow of QCD matter were investigated within the pQCD based 3+1 dimensional parton transport model BAMPS including bremsstrahlung $2 leftrightarrow 3$ processes. Within the same framework quenching
of gluonic jets in Au+Au collisions at RHIC can be understood. The development of conical structure by gluonic jets is investigated in a static box for the regimes of small and large dissipation. Furthermore we demonstrate two different approaches to extract the shear viscosity coefficient $eta$ from a microscopical picture.
Quenching of gluonic jets and heavy quark production in Au+Au collisions at RHIC can be understood within the pQCD based 3+1 dimensional parton transport model BAMPS including pQCD bremsstrahlung $2 leftrightarrow 3$ processes. Furthermore, the devel
opment of conical structures induced by gluonic jets is investigated in a static box for the regimes of small and large dissipation.
Employing a microscopic transport model we investigate the evolution of high energetic jets moving through a viscous medium. For the scenario of an unstoppable jet we observe a clearly strong collective behavior for a low dissipative system $eta/s ap
prox 0.005$, leading to the observation of cone-like structures. Increasing the dissipation of the system to $eta/s approx 0.32$ the Mach Cone structure vanishes. Furthermore, we investigate jet-associated particle correlations. A double-peak structure, as observed in experimental data, is even for low-dissipative systems not supported, because of the large influence of the head shock.
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 o
ut 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 $eta/s$. We also find that a good agreement between these two approaches requires a Knudsen number $Kn < 1/2$.
To investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic Riemann problem using a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by vary
ing the shear viscosity to entropy density ratio $eta/s$. We show that an $eta/s$ ratio larger than 0.2 prevents the development of well-defined shock waves on time scales typical for ultrarelativistic heavy-ion collisions. These findings are confirmed by viscous hydrodynamic calculations.
Fast thermalization and a strong buildup of elliptic flow of QCD matter as found at RHIC are understood as the consequence of perturbative QCD (pQCD) interactions within the 3+1 dimensional parton cascade BAMPS. The main contributions stem from pQCD
bremsstrahlung $2 leftrightarrow 3 $ processes. By comparing to Au+Au data of the flow parameter $v_2$ as a function of participation number the shear viscosity to entropy ratio is dynamically extracted, which lies in the range of 0.08 and 0.2, depending on the chosen coupling constant and freeze out condition. Furthermore, first simulations on the temporal propagation of dissipative shock waves are given. The cascade can either simulate true ideal shocks as well as initially diluted, truely viscous shocks, depending on the employed cross sections or mean free path, respectively.
