2001/01/25 by E. Abad, Patrick Grosfils, P. Grosfils +2 · 15 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Dynamical systems theory #Hierarchy #Lattice (music) #Limit (mathematics) #Master equation #Mathematical analysis #Mathematics #Mesoscopic physics #Nonlinear system #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #Stochastic dynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Truncation (statistics) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.63.041102
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 63(4), 041102 (American Physical Society) · 30 pages, 9 figures
arxiv created 2001/01/25 · openalex publication_date 2001/03/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a stochastic, time-discrete Boolean model that mimics the mesoscopic dynamics of the desorption reactions A+A-->A+S and A+A-->S+S in a one-dimensional lattice. In the continuous-time limit, we derive a hierarchy of dynamical equations for the subset of moments involving contiguous lattice sites. The solution of the hierarchy allows to compute the exact dynamics of the mean coverage for both microscopic and coarse-grained initial conditions, which turn out to be different from the mean field predictions. The evolution equations for the mean coverage and the second-order moments are shown to be equivalent to those provided by a time-continuous master equation. The important role of higher-order fluctuations is brought out by the failure of a truncation scheme retaining only two-particle fluctuation correlations.