The Bulk Viscosity of a Pion Gas

We compute the bulk viscosity of a gas of pions at temperatures below the QCD crossover temperature, for the physical value of pion mass, to lowest order in chiral perturbation theory. Bulk viscosity is controlled by number-changing processes which become exponentially slow at low temperatures when the pions become exponentially dilute, leading to an exponentially large bulk viscosity zeta ~ (F_0^8/m_\pi^5) exp(2m_\pi/T), where F_0 = 93 MeV is the pion decay constant.Comment: 13 pages, two figure

UV Cascade in Classical Yang-Mills via Kinetic Theory

We show that classical Yang-Mills theory with statistically homogeneous and isotropic initial conditions has a kinetic description and approaches a scaling solution at late times. We find the scaling solution by explicitly solving the Boltzmann equations, including all dominant processes (elastic and number-changing). Above a scale $p_{max} \propto t^{1/7}$ the occupancy falls exponentially in $p$. For asymptotically late times and sufficiently small momenta the occupancy scales as $f(p)\propto 1/p$, but this behavior sets in only at very late time scales. We find quantitative agreement of our results with lattice simulations, for times and momenta within the range of validity of kinetic theory.Comment: 18 pages, 4 figure

Thermalization of a QCD system via kinetic approach

The thesis is devoted to study the time evolution of an isotropic and homogeneous QCD system at extremely high energy scales. The numerical algorithm adopted in this research is the discrete momentum method, which is based on the Boltzmann equation in kinetic theory. Numerical simulations are performed in three scenarios: classical Yang-Mills field, pure gluon systems, and parton systems. The results confirm the parametric conclusions in recent studies. It shows that the thermalization time of an over-occupied system can be parametrized by a universal formula, but it is not true for a under-occupied system.Cette thèse est dévouée à l'étude de l'évolution temporelle d'un système de QCD isotropique et homogène à très haute ́énergie. L'algorithme numérique employé dans cette recherche est la méthode de la quantité de mouvement discrète qui est basée sur l'équation de Boltzmann dans la théorie cinétique des gaz. Des simulations numériques sont effectuées pour trois scénarios : pour un champ de Yang-Mills classique, pour un système de gluons pures, ainsi que pour un système de partons. Les résultats confirment les conclusions paramétriques des études récent. Il a également ́et ́e montré que le temps de thermalisation d'un système avec un très grand nombre d'occupation peut être paramétrisé par une formule universelle, mais il n'est pas vrai pour un système avec un très petit nombre d'occupation

Approach to equilibrium in weakly coupled nonabelian plasmas

We follow the time evolution of nonabelian gauge bosons from far-from-equilibrium initial conditions to thermal equilibrium by numerically solving an effective kinetic equation that becomes accurate in the weak coupling limit. We consider initial conditions that are either highly overoccupied or underoccupied. We find that overoccupied systems thermalize through a turbulent cascade reaching equilibrium in multiples of a thermalization time $t\approx 72./ (1-0.12\log \lambda)/\lambda^2 T$, whereas underoccupied systems undergo a "bottom-up" thermalization in a time $t\approx (34. +21. \ln(Q/T))/ (1-0.037\log \lambda)(Q/T)^{1/2}/\lambda^2 T$, where $Q$ is the characteristic momentum scale of the initial condition. We apply this result to model initial stages of heavy-ion collisions and find rapid thermalization roughly in a time $Qt \lesssim 10$ or $t\lesssim 1$ fm/c