The main focus of this article is to obtain various transport coefficients for a hot QCD medium that is produced while colliding two heavy nuclei ultra-relativistically. As the hot QCD medium follows dissipative hydrodynamics while undergoing space-time evolution, the knowledge of the transport coefficients such as thermal conductivity, electrical conductivity, shear and bulk viscosities are essential to understand the underlying physics there. The approach adopted here is semi-classical transport theory. The determination of all these transport coefficients requires knowledge of the medium away from equilibrium. In this context, we setup the linearized transport equation employing the Chapman-Enskog technique from kinetic theory of many particle system with a collision term that includes the binary collisions of quarks/antiquarks and gluons. In order to include the effects of a strongly interacting, thermal medium, a quasi-particle description of realistic hot QCD equation of state has been employed through the equilibrium modeling of the momentum distributions of gluons and quarks with non-trivial dispersion relations while extending the model for finite but small quark chemical potential. The effective coupling for strong interaction has been redefined following the charge renormalization under the scheme of the quasiparticle model. The consolidated effects on transport coefficients are seen to have significant impact on their temperature dependence. The relative significances of momentum and heat transfer as well as charge diffusion processes in hot QCD have been investigated by studying the ratios of the respective transport coefficients.

We evaluate the shear viscosity of a pion gas in the relativistic kinetic theory approach. The in-medium propagator of the ρ meson at finite temperature is used to evaluate the π − π scattering amplitude in the medium. The real and imaginary parts of the self-energy calculated from one-loop diagrams are seen to have noticeable effects on the scattering cross-section. The consequences on temperature dependence of the shear viscosity evaluated in the Chapman-Enskog and relaxation time approximations are studied.

The bulk and shear viscosities of a pion gas is obtained by solving the relativistic transport equation in the Chapman-Enskog approximation. In-medium effects are introduced in the $\pi\pi$ cross-section through one-loop self-energies in the propagator of the exchanged $\rho$ and $\sigma$ mesons. The effect of early chemical freeze-out in heavy ion collisions is implemented through a temperature dependent pion chemical potential. These are found to affect the temperature dependence of the bulk and shear viscosities significantly

In this article, shear viscosity, bulk viscosity, and thermal conductivity of a hot QCD medium have been studied in the presence of strong magnetic field. To model the hot magnetized QCD matter, an extended quasi-particle description of the hot QCD equation of state in the presence of the magnetic field has been adopted. The effects of higher Landau levels on the temperature dependence of viscous coefficients (bulk and shear viscosities) and thermal conductivity have been obtained by considering the 1 → 2 processes in the presence of the strong magnetic field. An effective covariant kinetic theory has been set up in (1+1)-dimensional that includes mean field contributions in terms of quasi-particle dispersions and magnetic field to describe the Landau level dynamics of quarks. The sensitivity of these parameters to the magnitude of the magnetic field has also been explored. Both the magnetic field and mean field contributions have seen to play a significant role in obtaining the temperature behaviour of the transport coefficients of hot QCD medium.

An effective relativistic kinetic theory has been constructed for an interacting system of quarks, anti-quarks and gluons within a quasi-particle description of hot QCD medium at finite temperature and baryon chemical potential, where the interactions are encoded in the gluon and quark effective fugacities with non-trivial energy dispersions. The local conservations of stress-energy tensor and number current require the introduction of a mean field term in the transport equation which produces non-vanishing contribution to the first order transport coefficients. Such contribution has been observed to be significant for the temperatures which are closer to the QCD transition temperature, however, induces negligible contributions beyond a few times the transition temperature. As an implication, impact of the mean field contribution on the the temperature dependence of the shear viscosity, bulk viscosity and thermal conductivity of a hot QCD medium in the presence of binary, elastic collisions among the constituents, has been investigated. Visible effects have been observed for the temperature regime closer to the QCD transition temperature.

We investigate the effect of the medium on the thermal conductivity of a pion gas out of chemical equilibrium by solving the relativistic transport equation in the Chapman-Enskog and relaxation time approximations. Using an effective model for the ππ cross-section involving ρ and σ meson exchange, medium effects are incorporated through thermal one-loop self-energies. The temperature dependence of the thermal conductivity is observed to be significantly affected.The observation of large elliptic flow of hadrons in heavy ion collisions at RHIC has led to the description of quark-gluon plasma as a nearly perfect fluid [1]. This interpretation is based on the small but finite value of the shear viscosity to entropy density ratio required in a relativistic hydrodynamic description of the collision. The effects of dissipation on the dynamical evolution of matter produced in relativistic heavy ion collisions have thus been a major topic of discussion in recent times [2]. At the microscopic level dissipative phenomena are studied by considering small departures from equilibrium. In kinetic theory the transport of momenta and heat as a result of collisions is quantitatively expressed in terms of coefficients of viscosity and thermal conductivity [3,4]. A large number of studies on the viscous coefficients have been performed in the transport approach. The shear viscosity η has been most commonly discussed followed by the bulk viscosity ζ, both for partonic as well as hadronic systems . The interesting issue concerning the behaviour of the viscosities in the vicinity of the transition from partonic to hadronic matter have also been discussed [1,12,14,15,[18][19][20]. While the value of η/s is expected to go through a minimum near the critical temperature [1, 18], ζ/s is believed to be large or diverging [12,15,19] at or near the transition.The effects of heat flow in heavy ion collisions has received much less attention. This is presumably on account of the fact that the net baryon number in the central rapidity region at the RHIC and LHC is very small. However, at FAIR energies or in the low energy runs at RHIC the baryon chemical potential is expected to be significant and heat conduction by baryons may play a more important role. On the other hand, a thermal system consisting of pions can sustain heat conduction despite the fact that the pions themselves do not carry baryon number [5]. This is due to the fact that the total number of pions in heavy ion collisions is essentially conserved. Pion number changing reactions are not sustained towards the late stages where collisions are mostly elastic and the system undergoes chemical freezeout. As the system expands and cools a pion chemical potential develops in order to keep the pion number fixed. Based on such a scenario a few studies of heat conduction by pions have been carried out. Using the experimental ππ cross-section the thermal conductivity of a pion gas was estimated in [5][6][7] whereas in [22] a unitarized scattering amplitude was employed. The heat conductiv...

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Collective excitations of a hot QCD medium are the main focus of the present article. The analysis is performed within semi-classical transport theory with isotropic and anisotropic momentum distribution functions for the gluonic and quark-antiquark degrees of freedom that constitutes the hot QCD plasma. The isotropic/equilibrium momentum distributions for gluons and quarks are based on a recent quasi-particle description of hot QCD equations of state. The anisotropic distributions are just the extensions of isotropic ones by stretching or squeezing them in one of the directions. The hot QCD medium effects in the model adopted here enter through the effective gluon and quark fugacities along with non-trivial dispersion relations leading to an effective QCD coupling constant. Interestingly, with these distribution functions the tensorial structure of the gluon polarization tensor in the medium turned out to be similar to the one for the non-interacting ultra-relativistic system of quarks/antiquarks and gluons . The interactions mainly modify the Debye mass parameter and , in turn, the effective coupling in the medium. These modifications have been seen to modify the collective modes of the hot QCD plasma in a significant way.