  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 single-time
Wigner function and study particle production starting from inhomogeneous
initial conditions. The particle numbers are compared with the Fermi-Dirac
distribution parametrized by a time dependent temperature and chemical
potential. We find that the fermions approximately thermalize locally in time.
