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Proposing Institution

Project Manager

Dr. Markus Michael Müller
Boltzmannstr. 1
85748 Garching
Boltzmann equations are often used to describe the non-equilibriumtime-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 the so-called Kadanoff-Baym equations. This raises the question how reliable Boltzmann equations are as approximations to full Kadanoff-Baym equations. Therefore, we performed a detailed comparison of Boltzmann and Kadanoff-Baym equations in the framework of relativistic quantum field theories in 3+1 space-time dimensions. In a first step, for simplicity we considered a real scalar Phi^4 quantum field theory and in a second step we generalized our results to a chirally invariant Yukawa-type quantum field theory including fermions. The obtained numerical solutions reveal significant discrepancies in the results predicted by both types of equations. Apart from quantitative discrepancies, on a qualitative level the universality respected by Kadanoff-Baym equations is severely restricted in the case of Boltzmann equations. Furthermore, Kadanoff-Baym equations strongly separate the time scales between kinetic and chemical equilibration. This separation of time scales is absent for Boltzmann equations. In this project we would like to continue our studies. The numerical solution of the above-mentioned Kadanoff-Baym equations requires a sophisticated optimization and parallelization of the algorithms as well as a corresponding high-performance computer hardware.

Impressum, Conny Wendler