Exact solution of the zero-range process: fundamental diagram of the corresponding exclusion process

Abstract

In this paper, we propose a general way of computing expectation values in the zero-range process, using an exact form of the partition function. As an example, we provide the fundamental diagram (the flux-density plot) of the asymmetric exclusion process corresponding to the zero-range process.We express the partition function for the steady state by the Lauricella hypergeometric function, and thereby have two exact fundamental diagrams each for the parallel and random sequential update rules. Meanwhile, from the viewpoint of equilibrium statistical mechanics, we work within the canonical ensemble but the result obtained is certainly in agreement with previous works done in the grand canonical ensemble.

12 pages, 2 figures

References in corpus (15)

• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Phase Transitions in one-dimensional nonequilibrium systems
• Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• The Nature of the Condensate in Mass Transport Models
• Canonical Analysis of Condensation in Factorised Steady State
• Condensation in the Backgammon model
• Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics
• Zero-range process with open boundaries
• A stochastic optimal velocity model and its long-lived metastability
• Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions
• On the ubiquity of matrix-product states in one-dimensional stochastic processes with boundary interactions
• Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring
• Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
• Analytical study on the criticality of the Stochastic Optimal Velocity model

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