Branching-annihilating random walks in one dimension: Some exact results

Abstract

We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast diffusion we obtain new information on the location and nature of the phase transition line between an active stationary state (non-zero density) and an absorbing state (extinction of all particles), thus clarifying some so far open problems. In these limits the transition is mean-field-like, but on the active side of the phase transition line the fluctuation in the number of particles deviates from its mean-field value. We also show that well within the active region of the phase diagram a finite system approaches the absorbing state very slowly on a time scale which diverges exponentially in system size.

8 pages; LaTex

References in corpus (12)

• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Theory of Branching and Annihilating Random Walks
• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Field Theory of Branching and Annihilating Random Walks
• Critical Exponents for Branching Annihilating Random Walks with an Even Number of Offspring
• One Dimensional Nonequilibrium Kinetic Ising Models with Branching Annihilating Random Walk
• Reaction-Diffusion Processes of Hard-Core Particles
• Non-equilibrium phase transitions in one-dimensional kinetic Ising models
• Propagation and Extinction in Branching Annihilating Random Walks
• The duality relation between Glauber dynamics and the diffusion-annihilation model as a similarity transformation
• Diffusion-limited annihilation in inhomogeneous environments
• Annihilating random walks in one-dimensional disordered media

Cited by in corpus (9)

• Universality classes in nonequilibrium lattice systems
• Branching and annihilating Levy flights
• A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0
• Surface Critical Behavior in Systems with Absorbing States
• The one-dimensional contact process: duality and renormalisation
• High-precision Estimate of the Critical Exponents for the Directed Ising Universality Class
• Surface Critical Behavior in Systems with Non-Equilibrium Phase Transitions
• Crossovers from parity conserving to directed percolation universality
• Block renormalization study on the nonequilibrium chiral Ising model