 
Summary: Particle production and effective thermalization in inhomogeneous mean field theory
Gert Aarts1
and Jan Smit1,2
1
Institute for Theoretical Physics, Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands
2
Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, the Netherlands
Received 29 June 1999; published 16 December 1999
As a toy model for dynamics in nonequilibrium quantum field theory we consider the Abelian Higgs model
in 1 1 dimensions with fermions. In the approximate dynamical equations, inhomogeneous classical mean
Bose fields are coupled to quantized fermion fields, which are treated with a mode function expansion. The
effective equations of motion imply e.g. Coulomb scattering, due to the inhomogeneous gauge field. The
equations are solved numerically. We define time dependent fermion particle numbers with the help of the
singletime Wigner function and study particle production starting from inhomogeneous initial conditions. The
particle numbers are compared with the FermiDirac distribution parametrized by a time dependent tempera
ture and chemical potential. We find that the fermions approximately thermalize locally in time.
PACS number s : 11.10.Kk, 05.70.Ln, 11.10.Wx, 11.15.Kc
I. INTRODUCTION
One issue that is of considerable interest in nonequilib
rium quantum field theory is equilibration and thermaliza
