Modelling one-dimensional driven diffusive systems by the Zero-Range Process

2004/05/04 by M. R. Evans, E. Levine, P. K. Mohanty +2 · 4 citations
Mathematics · Physics and Astronomy · #Spectroscopy and Quantum Chemical Studies #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1140/epjb/e2004-00314-7

published as Euro. Phys. J. B 41, 223 (2004).

arxiv created 2004/05/04 · openalex publication_date 2004/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The recently introduced correspondence between one-dimensional two-species driven models and the Zero-Range Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated through the length dependence of the current emitted from a particle domain. A direct numerical method for evaluating this current is introduced, and used to test the assumptions underlying this approach. In addition, a model for isolated domain dynamics is introduced, which provides a simple way to calculate the current also for the non-equal density case. This approach is demonstrated and applied to a particular two-species model, where a phase separation transition line is calculated.

Citations

• One-dimensional partially asymmetric simple exclusion process on a ring with a defect particle
• Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors
• Spatial particle condensation for an exclusion process on a ring

Cited by

• Condensation and coexistence in a two-species driven model
• Condensation in zero-range processes on inhomogeneous networks
• Phase separation transition of reconstitutingk-mers in one dimension
• Coarsening dynamics in a two-species zero-range process