Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

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Articles dans des revues à comité de lecture

Crossover properties of a one-dimensional reaction-diffusion process with a transport current
Fortin J.-Y.
Journal of Statistical Mechanics: Theory and Experiment 2014 (2014) P09033
ArXiv : arxiv:1402.6901 [PDF]
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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 [1] 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 [1], 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.

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