PROPAGATION AND EXTINCTION IN BRANCHING ANNIHILATING RANDOM-WALKS

We investigate the temporal evolution and spatial propagation of branc hing annihilating random walks (BAWs) in one dimension. Depending on t he branching and annihilation rates, a few-particle initial state can evolve to a propagating finite density wave, or an extinction may occu r, in which the number of particles vanishes in the long-time limit. T he number parity conserving case where two offspring are produced in e ach branching event can be solved exactly for a unit reaction probabil ity, from which qualitative features of the transition between propaga tion and extinction, as well as intriguing parity-specific effects, ar e elucidated. An approximate analysis is developed to treat this trans ition for general BAW processes. A scaling description suggests that t he critical exponents that describe the vanishing of the particle dens ity at the transition are unrelated to those of conventional models, s uch as Reggeon field theory.