Zero-range processes with saturated condensation: the steady state and dynamics

Abstract

We study a class of zero-range processes in which the real-space condensation phenomenon does not occur and is replaced by a saturated condensation: that is, an extensive number of finite-size "condensates" in the steady state. We determine the conditions under which this occurs, and investigate the dynamics of relaxation to the steady state. We identify two stages: a rapid initial growth of condensates followed by a slow process of activated evaporation and condensation. We analyze these nonequilibrium dynamics with a combination of meanfield approximations, first-passage time calculations and a fluctuation-dissipation type approach.

21 pages, 12 figures

References in corpus (13)

• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• 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
• Sand as Maxwell's demon
• Condensation in the zero range process: stationary and dynamical properties
• The Nature of the Condensate in Mass Transport Models
• Canonical Analysis of Condensation in Factorised Steady State
• Condensation in the Backgammon model
• Wealth Condensation in Pareto Macro-Economies
• Dynamics of the condensate in zero-range processes
• From urn models to zero-range processes: statics and dynamics
• Zero-Range Processes with Multiple Condensates: Statics and Dynamics

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• Finite size effects and metastability in zero-range condensation
• Generalizations of TASEP in discrete and continuous inhomogeneous space
• Flocking in One Dimension: Asters and Reversals
• Zero-range process with finite compartments: Gentile's statistics and glassiness
• Poisson-Dirichlet asymptotics in condensing particle systems
• Maintenance of order in a moving strong condensate