Segregation in diffusion-limited multispecies pair annihilation

Abstract

The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 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 rho(t) ~ t^{- alpha}. For d = 1 the system segregates into single species domains, yielding a different value of alpha for each q; for a simplified version of the model in one dimension we derive alpha(q) = (q-1) / (2q). Within mean-field theory, applicable in d >= 2, segregation occurs only for q < 1 + (4/d). The only physical realisation 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 (alpha = 1) that also characterises the single-species annihilation process A + A -> 0.

35 pages (IOP style files included), 10 figures included (as eps files)

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Cited by in corpus (8)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Master equations and the theory of stochastic path integrals
• Phase Transitions and Scaling in Systems Far From Equilibrium
• Symmetry and species segregation in diffusion-limited pair annihilation
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations
• Agent-based Monte Carlo simulations for reaction-diffusion models, population dynamics, and epidemic spreading
• Two-species diffusion-annihilation process on the fully-connected lattice: probability distributions and extreme value statistics