Annihilation reaction in a quasi-one-dimensional substrate

We study the annihilation reaction A+A→0 in a two-dimensional square lattice of width W and an infinite length. The behaviour of the density of particles ρ(t) is analyzed. This system exhibits a crossover time tc between the short-time (two-dimensional) and the long-time (one-dimensional) regimes. Using simple arguments and scaling functions we obtain an analytical expression of ρ(t) in the long-time regime which is in excellent agreement with Monte Carlo data, an approximation of ρ(t) for all times and the behaviour of tc as a function of W.