Tagged particle dynamics in one dimensional A plus A -> kA models with the particles biased to diffuse towards their nearest neighbour

Dynamical features of tagged particles are studied in a one dimensional system for k = 0 and 1, where the particles A have a bias to hop one step in the direction of their nearest neighboring particle. represents purely diffusive motion and represents purely deterministic motion of the particles. We show that for any , there is a time scale t* which demarcates the dynamics of the particles. Below t*, the dynamics are governed by the annihilation of the particles, and the particle motions are highly correlated, while for , the particles move as independent biased walkers. t* diverges as , where and . is a critical point of the dynamics. At , the probability , that a walker changes direction of its path at time t, decays as and the distribution of the time interval between consecutive changes in the direction of a typical walker decays with a power law as D(tau) similar to tau(-2).