Dynamical features of tagged particles are studied in a one dimensional A + A → kA system for k = 0 and 1, where the particles A have a bias ǫ (0 ≤ ǫ ≤ 0.5) to hop one step in the direction of their nearest neighboring particle. ǫ = 0 represents purely diffusive motion and ǫ = 0.5 represents purely deterministic motion of the particles. We show that for any ǫ, 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 t ≫ t * , the particles move as independent biased walkers. t * diverges as (ǫc − ǫ) −γ , where γ = 1 and ǫc = 0.5. ǫc is a critical point of the dynamics. At ǫc, the probability S(t), that a walker changes direction of its path at time t, decays as S(t) ∼ t −1 and the distribution D(τ ) of the time interval τ between consecutive changes in the direction of a typical walker decays with a power law as D(τ ) ∼ τ −2 .
We consider the dynamics of particles undergoing the reaction A + A → ∅ in one dimension with a dynamic bias. Here the particles move towards their nearest neighbour with probability 0.5 + where −0.5 < 0. c = −0.5 is the deterministic limit where the nearest neighbour interaction is strictly repulsive. We show that the negative bias changes drastically the behaviour of the fraction of surviving particles ρ(t) and persistence probability P(t) with time t. ρ(t) decays as a/(log t) b where b increases with − c . P(t) shows a stretched exponential decay with non-universal decay parameters. The probability Π(x, t) that a tagged particle is at position x from its origin is found to be Gaussian for all < 0; the associated scaling variable is x/t α where α approaches the known limiting value 1/4 as → c , in a power law manner. Some additional features of the dynamics by tagging the particles are also studied. The results are compared to the case of positive bias, a well studied problem.
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