Dynamics of condensation in the totally asymmetric inclusion process

Abstract

We study the dynamics of condensation of the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit, generalising recent results on finite lattices for symmetric dynamics. Our main focus is on totally asymmetric dynamics which have not been studied before, and which we also compare to exact solutions for symmetric systems. We identify all relevant dynamical regimes and corresponding time scales as a function of the system size, including a coarsening regime where clusters move on the lattice and exchange particles, leading to a growing average cluster size. Suitable observables exhibit a power law scaling in this regime before they saturate to stationarity following an exponential decay depending on the system size. Our results are based on heuristic derivations and exact computations for symmetric systems, and are supported by detailed simulation data.

23 pages, 6 figures, updated references and introduction

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• Derivation of mean-field equations for stochastic particle systems
• Explosive condensation in symmetric mass transport models
• A dynamical transition and metastability in a size-dependent zero-range process
• The exchange-driven growth model: basic properties and longtime behavior
• Mathematical Theory of Exchange-driven Growth
• Occupancy correlations in the asymmetric simple inclusion process
• Self-similar behavior of the exchange-driven growth model with product kernel
• A Unified Interface Model for Dissipative Transport of Bosons and Fermions
• Size-biased diffusion limits and the inclusion process
• Condensation in models with factorized and pair-factorized stationary states
• Second Time Scale of the Metastability of Reversible Inclusion Processes
• An algebraic approach to product-form stationary distributions for some reaction networks
• Large Time Behavior of Exchange-driven Growth
• A simple non-equilibrium, statistical-physics toy model of thin-film growth