Repelling Random Walkers in a Diffusion-Coalescence System
arXiv:0802.2699 · doi:10.1103/PhysRevE.77.031115
Abstract
We have shown that the steady state probability distribution function of a diffusion-coalescence system on a one-dimensional lattice of length L with reflecting boundaries can be written in terms of a superposition of double shock structures which perform biased random walks on the lattice while repelling each other. The shocks can enter into the system and leave it from the boundaries. Depending on the microscopic reaction rates, the system is known to have two different phases. We have found that the mean distance between the shock positions is of order L in one phase while it is of order 1 in the other phase.
5 pages, 1 EPS figure, Accepted for publication in PRE (2008)
References in corpus (13)
- Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
- Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension
- On Matrix Product Ground States for Reaction-Diffusion Models
- Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
- Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities
- Solution of a One-Dimensional Reaction-Diffusion Model with Spatial Asymmetry
- Shocks in the asymmetric exclusion process with internal degree of freedom
- Matrix Product States of Three Families of One-Dimensional Interacting Particle Systems
- Matrix Product Steady States as Superposition of Product Shock Measures in 1D Driven Systems
- Multiple Shocks in a Driven Diffusive System with Two Species of Particles
- Phase transitions in systems possessing Shock solutions
- Multi shocks in Reaction-diffusion models
- Exact Solution of a Reaction-Diffusion Model with Particle Number Conservation
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