Propagation and Extinction in Branching Annihilating Random Walks

Abstract

We investigate the temporal evolution and spatial propagation of branching annihilating random walks in one dimension. Depending on the branching and annihilation rates, a few-particle initial state can evolve to a propagating finite density wave, or extinction may occur, in which the number of particles vanishes in the long-time limit. The number parity conserving case where 2-offspring are produced in each branching event can be solved exactly for 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 which describe the vanishing of the particle density at the transition are unrelated to those of conventional models, such as Reggeon Field Theory. P. A. C. S. Numbers: 02.50.+s, 05.40.+j, 82.20.-w

12 pages, plain TeX

Cited by in corpus (32)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Theory of Branching and Annihilating Random Walks
• Field Theory of Branching and Annihilating Random Walks
• Stochastic Lattice Models with Several Absorbing States
• Quantitative Phase Diagrams of Branching and Annihilating Random Walks
• Universality Class of Two-Offspring Branching Annihilating Random Walks
• Pair contact process with diffusion - A new type of nonequilibrium critical behavior?
• Critical behaviour of the 1d annihilation fission process 2A->0, 2A->3A
• Critical phenomena of nonequilibrium dynamical systems with two absorbing states
• Reentrant phase diagram of branching annihilating random walks with one and two offsprings
• Binary spreading process with parity conservation
• Does hardcore interaction change absorbing type critical phenomena?
• A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
• Damage Spreading in the Ising Model
• Reaction-diffusion processes and non-perturbative renormalisation group
• Phase transition in a triplet process
• Critical behavior of roughening transitions in parity-conserving growth processes
• Stochastic cellular automaton for the coagulation-fission-process 2A->3A, 2A->A
• Branching-annihilating random walks in one dimension: Some exact results
• High-precision Estimate of the Critical Exponents for the Directed Ising Universality Class
• Phase transition between synchronous and asynchronous updating algorithms
• Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions
• Branching annihilating random walks with parity conservation on a square lattice
• On the Continuum Time Limit of Reaction-Diffusion Systems
• Kinetics of fragmentation-annihilation processes
• First order phase transition with a logarithmic singularity in a model with absorbing states
• Lattice Kinetics of Diffusion-Limited Coalescence and Annihilation with Sources
• Persistence in systems with conserved order parameter
• Block renormalization study on the nonequilibrium chiral Ising model
• Coarsening Dynamics of Nonequilibrium Chiral Ising Models
• Phase transition in a double branching annihilating random walk