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

We consider two single-species reaction-diffusion models on one-dimensional lattices of length L: the coagulation-decoagulation model and the annihilation model. For the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions. This system of differential equations grows quadratically with L in the latter case. The equations are solved analytically and exact expressions for the concentration are derived. We investigate the finite-size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions. We show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions. A similarity transformation between the two models is derived and used to connect the corresponding scaling functions.