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Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium

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Lindner,  Manfred
Division Prof. Dr. Manfred Lindner, MPI for Nuclear Physics, Max Planck Society;

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Müller,  Markus Michael
Division Prof. Dr. Manfred Lindner, MPI for Nuclear Physics, Max Planck Society;

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Citation

Lindner, M., & Müller, M. M. (2008). Comparison of Boltzmann Kinetics with Quantum Dynamics for a Chiral Yukawa Model Far From Equilibrium. Physical Review, D77: 025027, pp. 1-15. Retrieved from http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRVDAQ000077000002025027000001&idtype=cvips&gifs=yes.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-7A6A-E
Abstract
Boltzmann equations are often used to describe the non-equilibrium 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 Boltzmann and 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 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. 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.