Articles dans des revues à comité de lecture
|Crossover properties of a one-dimensional reaction-diffusion process with a transport current|
|Journal of Statistical Mechanics: Theory and Experiment 2014 (2014) P09033|
|ArXiv : arxiv:1402.6901 [PDF]|
1D non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equili brium dynamics, and fluctuation-dissipation relations. We consider in this paper transport properties in finite and semi-infinite one-dim ensional chains. A set of particles freely hop between nearest-neighbor sites, with the additional condition that, when two particles mee t, they merge instantaneously into one particle. A localized source of particle-current is imposed at the origin as well as a non-symmetr ic hopping rate between the left and right directions (particle drift). This model was previously studied with exact results for the part icle density by Hinrichsen et al  in the long-time limit. We are interested here in the crossover process between a scaling regime and long-time behavior, starting with a chain filled with particles. As in the previous reference , we employ the empty-interval-particle method, where the probability of finding an empty interval between two given sites is considered. However a different method is develope d here to treat the boundary conditions by imposing the continuity and differentiability of the interval probability, which allows for a closed and unique solution, especially for any given initial particle configuration. In the finite size case, we find a crossover between the scaling regime and two different exponential decays for the particle density as a function of the input current. Precise asymptotic expressions for the particle density and coagulation rate are given.