 
Summary: VOLUME 88, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 28 JANUARY 2002
Classical Aspects of Quantum Fields Far from Equilibrium
Gert Aarts and Jürgen Berges
Institut für Theoretische Physik, Philosophenweg 16, 69120 Heidelberg, Germany
(Received 16 July 2001; published 15 January 2002)
We consider the time evolution of nonequilibrium quantum scalar fields in the O N model, using
the nexttoleading order 1 N expansion of the twoparticle irreducible effective action. A compari
son with exact numerical simulations in 1 1 1 dimensions in the classical limit shows that the 1 N
expansion gives quantitatively precise results already for moderate values of N. For sufficiently high
initial occupation numbers the time evolution of quantum fields is shown to be accurately described by
classical physics. Eventually the correspondence breaks down due to the difference between classical
and quantum thermal equilibrium.
DOI: 10.1103/PhysRevLett.88.041603 PACS numbers: 11.10.Wx, 05.70.Ln, 11.15.Pg
In recent years we have witnessed an enormous increase
of interest in the dynamics of quantum fields out of equi
librium. Much progress has been achieved for systems
close to thermal equilibrium or with effective descriptions
based on a separation of scales in the weak coupling limit
[1]. Current and upcoming relativistic heavyion colli
sion experiments provide an important motivation to find
