Research Of Kinetic Theory In Quark-Gluon Plasma

Considerable attention has been paid on the mechanism of the formation and the evolution of the QGP and many valuable models have appeared. The fundamental theoretic methods dealing with the QGP are the finite-temperature field theory, the kinetic theory and phenomenological analysis. The kinetic theory is a statistical theory that can deal with both the thermal equilibrium and the non-equilibrium phenomena. The kinetic equations for the QGP have been formed under the general frame of the statistical theory and its dynamic basic is the quantum chromodynamics (QCD), which the component particles of the system obey. They are widely used to investigate the properties of the QGP. The kinetic theory is admitted generally since it has been shown that the kinetic theory is equal to the temperature field theory in the HTL's.The QGP, if formed in the relativistic heavy ion collisions, is generallybelieved to be in a thermal non-equilibrium state during initial stage, so it is important to study non-equilibrium phenomena in the QGP. According to statistical mechanics, if the particle distribution function of the system is known, any observable physical quantities can be obtained through standard method. Hence, the non-equilibrium distribution function is the basis of solving non-equilibrium problems. Unfortunately, it is difficult to obtain the non-equilibrium distribution functions by strictly solving the QGP kinetic equations. However, when the fluctuation of the color field in the QGP is at the gT level, many properties of the QGP in quasi-equilibrium have been discussed in the QGP kinetic equations without collision integrals.In Chapter 3, we calculate the distribution functions in the QGP kinetic equations under this approximation, and assume that the perturbation of the color field fluctuation is at the gT level and the fluctuation makes the QGP in a non-equilibrium state. Then the distribution function in quasi-equilibrium can be obtained by using a step-by-step iteration method, namely derivative expansion. In this chapter, we start from the kinetic equation, approximate the collision integral as relaxion-time approximation and obtain the distribution function of the quark, anti-quark and gluon by using approximation method. Through numerical analysis we discuss the characteristics of the distribution functions of component particles in the QGP: at any given single particle energy e, the value of the quark distributions function in quasi-equilibrium solid is larger than that of the corresponding distribution functions in equilibrium (the dashing line). The higher the temperature is, the larger thedifference between the two kinds of distribution functions is. Figl also shows that the distinct difference exists near the Fermi surface. The curve transfers upward if the relaxation time of the system becomes longer. It means that the difference between the distribution functions in quasi-equilibrium and in equilibrium is larger if the system needs more time to attain the equilibrium state. The curves of gluon distribution function in quasi-equilibrium are away from that of the according distribution functions in equilibrium, and the higher the temperature is, the more obvious the tendency of deviation is. In addition, the smaller the gluon energy is, the larger the deviation is. The curve transfers downward if the relaxation time becomes longer. It means that when the system takes longer relaxation time, the gluon distribution function is farther to its according equilibrium function.In Chapter 5, noting that the QGP produced in the experiment is in a non-equilibrium state. There are many physical scenarios in non-equilibrium and transport phenomenon is one of them.Therefore it is important to calculate transport coefficients. We still start from the QGP semi-classical kinetic equation, approximate the collision integral as relaxion-time but assume that the system is near the local equilibrium state, and then we compare the energy-momentum tensor obtained from statistical physics with the correspon...