Comparison of Boltzmann equations with quantum dynamics for scalar fields

Abstract

References (55)

Citing Articles

Download: PDF (502 kB) or Buy this Article (US$25) (Use Article Pack)

Manfred Lindner¹ and Markus Michael Müller^1,2
¹Physik-Department T30d, Technische Universität München, James-Franck-Straße, 85748 Garching, Germany
²Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München, Germany

Received 13 January 2006; published 5 June 2006

Boltzmannequations are often used to study the thermal evolution ofparticle reaction networks. Prominent examples are the computation of thebaryon asymmetry of the universe and the evolution of thequark-gluon plasma after relativistic heavy ion collisions. However, Boltzmann equationsare only a classical approximation of the quantum thermalization processwhich is described by the so-called Kadanoff-Baym equations. This raisesthe question how reliable Boltzmann equations are as approximations tothe full Kadanoff-Baym equations. Therefore, we present in this papera detailed comparison between the Kadanoff-Baym and Boltzmann equations inthe framework of a scalar Phi⁴ quantum field theory in3+1 space-time dimensions. The obtained numerical solutions reveal significant discrepanciesin the results predicted by both types of equations. Apartfrom quantitative discrepancies, on a qualitative level the universality respectedby the Kadanoff-Baym equations is severely restricted in the caseof Boltzmann equations. Furthermore, the Kadanoff-Baym equations strongly separate thetime scales between kinetic and chemical equilibration. This separation oftime scales is absent for the Boltzmann equation.

URL:	http://link.aps.org/doi/10.1103/PhysRevD.73.125002
DOI:	10.1103/PhysRevD.73.125002
PACS:	11.10.Wx; 12.38.Mh; 98.80.Cq 11.10.Wx Finite-temperature field theory 12.38.Mh Quark–gluon plasma 98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.) YEAR: 2006
KEYWORDS:	Boltzmann equation, quark-gluon plasma, heavy ion-nucleus reactions, phi4 field theory

REFERENCES (55)

View in Separate Window/Tab

For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.

J. Berges, S. Borsányi, and C. Wetterich, Phys. Rev. Lett. 93, 142002 (2004).
Sangyong Jeon, Phys. Rev. C 72, 014907 (2005).
Gert Aarts and Jürgen Berges, Phys. Rev. D 64, 105010 (2001).
H. S. Köhler, Phys. Rev. C 51, 3232 (1995).
S. Juchem, W. Cassing, and C. Greiner, Phys. Rev. D 69, 025006 (2004).
Gordon Baym and Leo P. Kadanoff, Phys. Rev. 124, 287 (1961).
Gordon Baym, Phys. Rev. 127, 1391 (1962).
R. Jackiw, Phys. Rev. D 9, 1686 (1974).
John M. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974).
E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1988).
Gert Aarts and Jürgen Berges, Phys. Rev. Lett. 88, 041603 (2002).
Gert Aarts and Jose M. Martínez Resco, Phys. Rev. D 68, 085009 (2003).
J. Berges, Sz. Borsányi, U. Reinosa, and J. Serreau, Phys. Rev. D 71, 105004 (2005).
Alejandro Arrizabalaga, Jan Smit, and Anders Tranberg, Phys. Rev. D 72, 025014 (2005).
Hendrik van Hees and Jörn Knoll, Phys. Rev. D 65, 025010 (2002).
Hendrik van Hees and Jörn Knoll, Phys. Rev. D 65, 105005 (2002).
Hendrik van Hees and Jörn Knoll, Phys. Rev. D 66, 025028 (2002).
Julian S. Schwinger, J. Math. Phys. (N.Y.) 2, 407 (1961).
Pradip M. Bakshi and Kalyana T. Mahanthappa, J. Math. Phys. (N.Y.) 4, 1 (1963).
Pradip M. Bakshi and Kalyana T. Mahanthappa, J. Math. Phys. (N.Y.) 4, 12 (1963).