Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions
Résumé
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.
Mots clés
Heavy Ion Phenomenology
Phenomenological Models
quark gluon: plasma
approximation: small-angle
viscosity: correction
pressure: transverse
momentum: anisotropy
heavy ion: scattering
hydrodynamics
distribution function
Boltzmann equation
momentum spectrum
longitudinal
thermal
kinetic
numerical calculations