1994/05/10 by Daniel ben‐Avraham, Daniel ben-Avraham, Francois Leyvraz +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physreve.50.1843
published as Phys. Rev. E 50, 1843 (1994). · 12 pages, plain TeX
arxiv created 1994/05/10 · openalex publication_date 1994/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the temporal evolution and spatial propagation of branching annihilating random walks (BAWs) in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite density wave, or an extinction may occur, in which the number of particles vanishes in the long-time limit. The number parity conserving case where two offspring are produced in each branching event can be solved exactly for a unit reaction probability, from which qualitative features of the transition between propagation and extinction, as well as intriguing parity-specific effects, are elucidated. An approximate analysis is developed to treat this transition for general BAW processes. A scaling description suggests that the critical exponents that describe the vanishing of the particle density at the transition are unrelated to those of conventional models, such as Reggeon field theory.