Segregation in diffusion-limited multispecies pair annihilation

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2004-07-16

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IOP

Abstract

The kinetics of the q species pair annihilation reaction (Ai + Aj → ∅ for 1 ≤ i < j ≤ q) in d dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as ρ(t) ∼ t-∞. For d = 1 the system segregates into single species domains, yielding a different value of α for each q; for a simplified version of the model in one dimension we derive α(q) = (q − 1)/(2q). Within mean-field theory, applicable in d ≥ 2, segregation occurs only for q < 1 + (4/d). The only physical realization of this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed by an extra local conservation law. For d ≥ 2 and q ≥ 1 + (4/d) the system remains disordered and its density is shown to decay universally with the mean-field power law (α = 1) that also characterizes the single-species annihilation process A + A → ∅.

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Keywords

Physics, Multidisciplinary, Physics, Mathematical, Physics, RENORMALIZATION-GROUP, SPECIES ANNIHILATION, PHASE-TRANSITIONS, SPATIAL STRUCTURE, QUANTUM CHAINS, FIELD, PARTICLE, KINETICS, BEHAVIOR, DYNAMICS

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