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One-dimensional non-equilibrium models of particles subjected to acoagulation-diffusion process are important in understanding non-equilibriumdynamics, and fluctuation-dissipation relation. We consider in this papertransport properties in finite and semi-infinite one-dimensional chains. A setof particles freely hop between nearest-neighbor sites, with the additionalcondition that, when two particles meet, they merge instantaneously into oneparticle. A localized source of particle-current is imposed at the origin aswell as a non-symmetric hopping rate between the left and right directions(particle drift). This model was previously studied with exact results for theparticle density by Hinrichsen et al. [1] in the long-time limit. We areinterested here in the crossover process between a scaling regime and long-timebehavior, starting with a chain filled of particles. As in the previousreference [1], we employ the empty-interval-particle method, where theprobability of finding an empty interval between two given sites is considered.However a different method is developed here to treat the boundary conditionsby imposing the continuity and differentiability of the interval probability,which allows for a closed and unique solution, especially for any given initialparticle configuration. In the finite size case, we find a crossover betweenthe scaling regime and two different exponential decays for the particledensity as function of the input current. Precise asymptotic expressions forthe particle-density, and coagulation rate are given.

Crossover properties of a one-dimensional reaction-diffusion process with a transport current