Diffusion-limited coagulation in the presence of particle input: Exact results in one dimension

We solve the diffusion-limited single-species coagulation process (A+A{→}A) with random particle input in one spatial dimension. We derive the exact time-dependent concentration, the spectrum of relaxation rates, and the distribution of interparticle distances in the nonequilibrium steady state. These results imply an interesting microscopic spatial structure induced by the nonequilibrium constraints. The validity of rate-equation descriptions of the macroscopic statics and kinetics is investigated, and we compare our results to the closely related single-species annihilation process (A+A{→}inert) in the presence of input.