Coarsening dynamics in condensing zero-range processes and size-biased birth death chains
arXiv:1511.09357 · doi:10.1088/1751-8113/49/18/185005
Abstract
Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest. Starting from homogeneous initial conditions, the time evolution of the condensed phase exhibits an interesting coarsening phenomenon of mass transport between cluster sites characterized by a power law. We revisit the approach in [C. Godreche, J. Phys. A: Math. Gen., 36(23) 6313 (2003)] to derive effective single site dynamics which form a non-linear birth death chain describing the coarsening behaviour. We extend these results to a larger class of parameter values, and introduce a size-biased version of the single site process, which provides an effective tool to analyze the dynamics of the condensed phase without finite size effects and is the main novelty of this paper. Our results are based on a few heuristic assumptions and exact computations, and are corroborated by detailed simulation data.
In addition to some minor changes, Figure 7(a) and the text below have been adapted to correct a mistake in the published version, pointed out to us by C. Godreche
References in corpus (3)
Cited by in corpus (8)
- Structure of the condensed phase in the inclusion process
- Coarsening dynamics of zero-range processes
- Derivation of mean-field equations for stochastic particle systems
- Mathematical Theory of Exchange-driven Growth
- Steady states in a non-conserving zero-range process with extensive rates as a model for the balance of selection and mutation
- Self-similar behavior of the exchange-driven growth model with product kernel
- The role of zero-clusters in exchange-driven growth with and without input
- Condensation in zero-range processes with a fast rate