FINITE-SIZE-SCALING STUDIES OF ONE-DIMENSIONAL REACTION-DIFFUSION SYSTEMS .1. ANALYTICAL RESULTS

We consider two single-species reaction-diffusion models on one-dimens ional lattices of length L: the coagulation-decoagulation model and th e annihilation model. For the coagulation model the system of differen tial equations describing the time evolution of the empty interval pro babilities is derived for periodic as well as for open boundary condit ions. This system of differential equations grows quadratically with L in the latter case. The equations are solved analytically and exact e xpressions for the concentration are derived. We investigate the finit e-size behavior of the concentration and calculate the corresponding s caling functions and the leading corrections for both types of boundar y conditions. We show that the scaling functions are independent of th e initial conditions but do depend on the boundary conditions. A simil arity transformation between the two models is derived and used to con nect the corresponding scaling functions.