2003/02/28 by Stefan Grosskinsky, Stefan Großkinsky, Gunter M. Schütz +2 · 5 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Cluster analysis #Diffusion and Search Dynamics #Domain (mathematical analysis) #Jump #Jump process #Measure (data warehouse) #Monte Carlo method #Range (aeronautics) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Zero (linguistics) #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1023/a:1026008532442
published as J. Stat. Phys. 113(3/4), 389-410 (2003) · 22 pages, 4 figures, to appear in J. Stat. Phys.; improvement of presentation and content of Theorem 2, added references
arxiv created 2003/06/06 · openalex publication_date 2003/10/24 · openalex created_date 2016/06/24 · arxiv updated 2018/04/26 · openalex updated_date 2026/08/05
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.