Comparison of Boltzmann kinetics with quantum dynamics for a chiral Yukawa model far from equilibrium
M. Lindner, Markus Michael Müller
Boltzmann equations are often used to describe the nonequilibrium time-evolution of many-body systems in particle physics. Prominent examples are the computation of the baryon asymmetry of the universe and the evolution of the quark-gluon plasma after a relativistic heavy ion collision. However, Boltzmann equations are only a classical approximation of the quantum thermalization process, which is described by so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to the complete Kadanoff-Baym equations. Therefore, we present in this article a detailed comparison of the Boltzmann and the Kadanoff-Baym equations in the framework of a chirally invariant Yukawa-type quantum field theory including fermions and scalars. The obtained numerical results reveal significant differences between both types of equations. Apart from quantitative differences, on a qualitative level the late-time universality respected by the Kadanoff-Baym equations is severely restricted in the case of the Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. In contrast to this standard Boltzmann equations cannot describe the process of quantum-chemical equilibration, and consequently also cannot feature the above separation of time scales.
arXiv:0710.2917•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jan 28, 2008•32 citations