Diffusion-annihilation in the presence of a driving field

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+or- eta )/2 to the right and left nearest neighbouring site respectively if this site is vacant, and annihilate with rate one if it is occupied. We show that density fluctuations (i.e. the mth moments (N m ) of the density distribution at time t) do not depend on the spatial anisotropy eta 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 eta . In the scaling regime t approximately L 2 the effect of the driving can be completely absorbed in a Galilei transformation. 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 t 0 =0.