2014/02/28 by Jean-Yves Fortin · 6 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Boundary value problem #Crossover #Differentiable function #Diffusion and Search Dynamics #Dissipation #Exponential function #Geometry #Mathematical analysis #Mathematics #Particle (ecology) #Particle density #Periodic boundary conditions #Physics #Quantum mechanics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/2014/09/p09033
published in Journal of Statistical Mechanics Theory and Experiment 2014(9), P09033 (Institute of Physics) · 23 pages, 8 figures
openalex publication_date 2014/09/30 · arxiv created 2014/10/01 · arxiv updated 2015/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
1D non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relations. We consider in this paper transport properties in finite and semi-infinite one-dimensional chains. A set of particles freely hop between nearest-neighbor sites, with the additional condition that, when two particles meet, they merge instantaneously into one particle. A localized source of particle-current is imposed at the origin as well as a non-symmetric hopping rate between the left and right directions (particle drift). This model was previously studied with exact results for the particle 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 developed 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.