Abstract
The pre-equilibrium evolution of a quark-gluon plasma produced in a heavy-ion collision is studied in the framework of kinetic theory. We discuss the approach to local thermal equilibrium, and the onset of hydrodynamics, in terms of a particular set of moments of the distribution function. These moments quantify the momentum anisotropies to a finer degree than the commonly used ratio of longitudinal to transverse pressures. They are found to be in direct correspondence with viscous corrections of hydrodynamics, and provide therefore an alternative measure of these corrections in terms of the distortion of the momentum distribution. As an application, we study the evolution of these moments by solving the Boltzmann equation for a boost invariant expanding system, first analytically in the relaxation time approximation, and then numerically for a quark-gluon plasma with a collision kernel given by leading order 2 ↔ 2 QCD matrix elements in the small angle approximation.
Highlights
Possible to recast the solution of the Boltzmann equation in terms of an infinite hierarchy of equations for a particular set of moments of the distribution function
We study the evolution of these moments by solving the Boltzmann equation for a boost invariant expanding system, first analytically in the relaxation time approximation, and numerically for a quark-gluon plasma with a collision kernel given by leading order 2 ↔ 2 QCD matrix elements in the small angle approximation
Near the hydrodynamic regime, these moments are in correspondence to the viscous corrections that emerge from a gradient expansion
Summary
After a brief review of the main features of expanding boost invariant systems, we define a set of moments of the distribution function that are suited to the. Near the hydrodynamic regime, these moments are in correspondence to the viscous corrections that emerge from a gradient expansion
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