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

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.

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Cited by in corpus (25)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Canonical Analysis of Condensation in Factorised Steady State
• Dynamics of the condensate in zero-range processes
• Condensation in stochastic mass transport models: beyond the zero-range process
• Explosive condensation in a mass transport model
• Long-range attraction between probe particles mediated by a driven fluid
• Condensation in zero-range processes on inhomogeneous networks
• Particle Ordering in Zero Range Process : Exact spatial correlations of the corresponding exclusion models
• Nonexistence of motility induced phase separation transition in one dimension
• Dynamics of Shock Probes in Driven Diffusive Systems
• Shock probes in a one-dimensional Katz-Lebowitz-Spohn model
• Condensation and coexistence in a two-species driven model
• Coarsening dynamics in a two-species zero-range process
• Dynamical scaling for probe particles in a driven fluid
• Assisted exchange models in one dimension
• Cluster-factorized steady states in finite range processes
• Phase separation transition of reconstituting k-mers in one dimension
• On Random Allocation Models in the Thermodynamic Limit
• Zero range and finite range processes with asymmetric rate functions
• Phase separation transition in anti-ferromagnetically interacting particle systems
• Phase coexistence and spatial correlations in reconstituting k-mer models
• Matrix Product States for Interacting Particles without Hardcore Constraints
• Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions
• Condensation transition in a conserved generalized interacting zero-range process