ANNIHILATION REACTIONS - CROSSOVER FROM MEAN-FIELD TO ANOMALOUS BEHAVIORS

We study the coagulation reaction A + A --> A with diffusion and proba bility p of reaction in a one dimensional lattice and the annihilation reaction A + A --> 0 with diffusion and interaction in the two-dimens ional fractal percolation cluster. Due to reaction the particle densit y rho decreases as a function of time t. The crossover from mean-field (rho similar to t(-1)) to anomalous behaviors (rho similar to t(-1/2) in one dimension and rho similar to t(-2/3) in the percolation cluste r) is analyzed. From this analysis, in one dimension an analytical app roximation of the density is found which agrees very well with Monte C arlo results of rho(t) for all times and for small values of p. For th e percolation cluster and large values of the nearest-neighbor repulsi ve interaction U between particles, we find that a simple mean-field a pproximation works at short times. The length of the time interval whe re this approximation holds increases as U increases.