We study the effect of an external driving force on a simple stochastic
reaction-diffusion system in one dimension. In our model each lattice site may
be occupied by at most one particle. These particles hop with rates
(1±η)/2 to the right and left nearest neighbouring site resp. if this
site is vacant and annihilate with rate 1 if it is occupied. We show that
density fluctuations (i.e. the mth moments ⟨Nm⟩ of the
density distribution at time t) do not depend on the spatial anisotropy
η induced by the driving field, irrespective of the initial condition.
Furthermore we show that if one takes certain translationally invariant
averages over initial states (e.g. random initial conditions) even local
fluctuations do not depend on η. In the scaling regime t∼L2 the
effect of the driving can be completely absorbed in a Galilei transformation
(for any initial condition). We compute the probability of finding a system of
L sites in its stationary state at time t if it was fully occupied at time
t0=0.Comment: 17 pages, latex, no figure