Transport coefficients and early time dynamics of the Quark-Gluon Plasma created in ultra-relativistic heavy ion collisions

Abstract

The phase diagram of QCD is actually under exploration both theoretically and experimentally searching for the phase transition from ordinary matter to a deconfined phase of quarks and gluons, namely the Quark-Gluon Plasma. Being a very complex theory, such a task is very difficult however there are several indications that the phase transition occurs as indicated by Lattice QCD calculations, in the low baryon density region, at a critical temperature of Tc 155 MeV. The only way to access the QGP in a laboratory is to collide heavy ion collision at ultra-relativistic (uRHIC) energies as actually carry out at LHC at CERN and at RHIC at BNL. One of the most amazing discovery was that the system created in these collisions behaves like a perfect fluid. Indeed hydrodynamics calculations show that the large anisotropic flows measured are in agreement with a shear viscosity to entropy density ration eta/s close to the minimum value predicted by AdS/CFT eta/s = 1/4pi. In this thesis we discuss about two main subjects of QGP produced in uRHIC: transport coefficients, in particular shear viscosity and electric conductivity, and a modeling of initial fields and their early time dynamics of the system produced in uRHIC. Our challenge is to develop a very precise transport based approach with a fixed value of eta/s, being the physical quantity that describes a fluid in strong coupling. We compute the shear viscosity solving the Relativistic Boltzmann Transport (RBT) equation and using the Green-Kubo relation that, being not affected by any kind of approximation, gives us the possibility to find the correct formula among the analytical derivations in Relaxation Time Approximation and in Chapman-Enskog scheme. Using our numerical solution to the RTB equation we also compute the electric conductivity sigma-el of the QGP. This transport coefficient represents the response of the system to an applied external electric field and only very recently has captured the attention in the field of QGP due to the strong electric and magnetic fields present in the early stage of the collision. Our focus was to characterize the relation between the sigmael and the relaxation time tau . Moreover we study the relationship between eta and sigmael investigating the ratio between eta/s and sigma-el/T, taking into account the QCD thermodynamics, and predicting that the ratio supplies a measure of the quark to gluon scattering rates. Once we have developed a transport based approach describing a fluid with a given eta/s, our interest moved into describing, using a single consistent approach, the fireball created in uRHIC starting from the initial time. We modeled the early time dynamics considering only a color electric field which decays to pair particles thanks to the Schwinger mechanism. Our studies focused on the isotropization and thermalization of the system in the early stage in order to quantify the isotropization time, which is assumed to be tau-iso = 0.6 ÷ 0.8 f m/c in hydrodynamics calculations. We investigate in a sistematic way different systems: the static box, the longitudinal expanding system and the 3+1D expanding case. We compute the ratio PL/PT , with PL (PT ) the longitudinal (transverse) pressure, finding that for the relevant cases of 1+1D and 3+1D the system reaches PL/PT about 1, which characterizes the isotropization of the system, in about 1fm/c for eta/s = 1/4pi while for higher value of shear viscosity the ratio PL/PT is quite smaller than 1, meaning that the system does not isotropize. Moreover we study also the effects of eta/s on the elliptic flow v2. The first studies show that the final v2 developed by the system is not significantly affected by the strong early non-equilibrium dynamics. Hence, such a result provides a justification of the assumptions exploited in hydrodynamical approach.