  We discuss a reaction-diffusion model in one dimension subjected to an
external driving force. Each lattice site may be occupied by at most one
particle. The particles hop with asymmetric rates (the sum of which is one) to
the right or left nearest neighbour site if it is vacant, and annihilate with
rate one if it is occupied.
  We compute the long time behaviour of the space dependent average density in
states where the initial density profiles are step functions. We also compute
the exact time dependence of the particle density for uncorrelated random
initial conditions. The representation of the uncorrelated random initial state
and also of the step function profile in terms of free fermions allows the
calculation of time-dependent higher order correlation functions. We outline
the procedure using a field theoretic approach.

Condensed Matter;Chemical Physics