One of the main results of heavy ions collision at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower ...bound η/s 1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green- Kubo relations give us an exact expression to compute these coefficients. We computed shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigated different cases of particles, for one component system (gluon matter), interacting via isotropic or anisotropic cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. Another transport coefficient of interest is the electric conductivity σel which determines the response of QGP to the electromagnetic fields present in the early stage of the collision. We study the σel dependence on microscopic details of interaction and we find also in this case that Relaxation Time Approximation is a good approximation only for isotropic cross-section.
In this study we model early time dynamics of relativistic heavy ion collisions by an initial color-electric field which then decays to a plasma by the Schwinger mechanism. The dynamics of the many ...particles system produced by the decay is described by relativistic kinetic theory, taking into account the backreaction on the color field by solving self-consistently the kinetic and the field equations. Our main results concern isotropization and thermalization for a 1+1D expanding geometry. In case of small η/s (η/s ≲ 0.3) we find τisotropization ≈ 0.8 fm/c and τthermalization ≈ 1 fm/c in agreement with the common lore of hydrodynamics.
The propagation of heavy flavor through the quark gluon plasma has been treated commonly within the framework of Langevin dynamics, i.e. assuming the heavy flavor momentum transfer is much smaller ...than the light one. On the other hand a similar suppression factor RAA has been observed experimentally for light and heavy flavors. We present a thorough comparison in terms of nuclear suppression, RAA, elliptic flow, v2, and c back to back correlation between the Langevin equation and the full collisional Boltzmann collision integral within the framework of Boltzmann transport equation. We have shown that the Langevin dynamics overestimates the interaction and even for a fixed RAA the full two-body collision integral shows that the elliptic flow is larger with respect to that predicted by a Langevin dynamics. Furthermore we have found that Boltzmann approach gives rise to a larger spreading of c correlation in comparison with the Langevin approach.
We have employed a relativistic kinetic transport approach that incorporates initial state fluctuations to study the effect of a temperature dependent shear viscosity to entropy density ratio η/s(T) ...on the build-up of the anisotropic flows υn(pT). We find that at LHC energies and for ultra-central collisions (0 – 0.2%) the υn(pT) have a stronger sensitivity to the T dependence of η/s in the QGP phase and this sensitivity increases with the order of the harmonic n. Moreover we have studied the correlation between the initial spatial anisotropies ϵn and the final flow coefficients (υn) for different centralities and for the two beam energies. The study shows that at LHC energies there is more correlation than at RHIC energies. In particular at LHC energies and for ultra-central collisions the linear correlation coefficient C(ϵn, υn) ≈ 1 for n = 2, 3, 4 and 5 suggesting that the (υn) are strongly related to the initial value of ϵn.
We present numerical results of electric conductivity sigma sub(el) of a fluid obtained solving the relativistic transport Boltzmann equation in a box with periodic boundary conditions. We compute ...sigma sub(el) using two methods: the definition itself, i.e., applying an external electric field, and the evaluation of the Green-Kubo relation based on the time evolution of the current-current correlator. We find a very good agreement between the two methods. We also compare numerical results with analytic formulas in relaxation time approximation (RTA) where the relaxation time for sigma sub(el) is determined by the transport cross section sigma sub(tr), i.e., the differential cross section weighted with the collisional momentum transfer. We investigate the electric conductivity dependence on the microscopic details of the two-body scatterings: isotropic and anisotropic cross section as well as massless and massive particles. We find that the RTA underestimates considerably sigma sub(el); for example, at screening masses mD ~ T, such underestimation can be as large as a factor of 2. Furthermore, we study a more realistic case for a quark-gluon system (QGP) considering both a quasiparticle model tuned to lattice QCD (IQCD) thermodynamics, as well as the case of a perturbative QCD (pQCD) gas with running coupling. Also, for these cases more directly related to the description of the QGP system, we find that the RTA significantly underestimates the sigma sub(el) by about 60%-80%.
We study the build up of elliptic flow v2 and high order harmonics vn within a transport approach at fixed shear viscosity to entropy density ratio η/s and with initial state fluctuations. In ...particular we study the effect of a temperature dependent η/s for two different beam energies: RHIC for Au+Au at 200 GeV and LHC for Pb + Pb at 2.76 TeV. We find that for the two different beam energies considered the suppression of the elliptic flow and of higher harmonics v3(pT) and v4(pT) due to the viscosity of the medium have different contributions coming from the cross over or QGP phase. Moreover, we discuss the correlation between the initial spatial anisotropies εn and flow coefficients vn. We observe that the elliptic flow v2 is strongly correlated with initial eccentricity ε2. While higher harmonics v3 and v4 are weakly correlated to their asymmetry measure in coordinate space ε3 and ε4.
In this talk, we report on our results about the computation of isotropization and thermalization times of the quark-gluon plasma produced in relativistic heavy ion collisions, as well as of the ...elliptic flow. Simulation of the evolving fireball is achieved by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio eta/s. Our results show that the saturation in the initial spectrum reduces the efficiency in building-up the elliptic flow. Moreover both thermalization and isotropization times are quite small, approximately of 1 fm/c, if the system is in a strong coupling regime.
We use a relativistic transport approach to study the role of a temperature dependent shear viscosity to entropy density ratio, η/s(T), on the build-up of the elliptic flow, v2. The recent results ...from = 62.4GeV at RHIC up to 2.76 TeV at LHC have shown an intriguing property of the v2(pT), which appears to be nearly invariant with energy. We show that in our transport approach this surprising behavior can be described by a particular temperature dependence of η/s(T), typical of matter that undergoes a phase transition or a cross-over, with a rise and fall and the minimum close to critical temperature Tc.
The two key observables related to heavy quarks that have been measured in experiments are the nuclear suppression factor RAA and the elliptic flow ν2. The simultaneous reproduction of these two ...observables is a puzzle which have challenged all the existing models. We discuss two ingredients responsible for addressing a large part of such a puzzle: the temperature dependence of the energy loss and the full solution of the Boltzmann collision integral for the scattering between the heavy quarks and the particle of the bulk.
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