Symmetry and species segregation in diffusion-limited pair annihilation

Abstract

We consider a system of q diffusing particle species A_1,A_2,...,A_q that are all equivalent under a symmetry operation. Pairs of particles may annihilate according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the symmetry, and without self-annihilation (k_{ii} = 0). In spatial dimensions d > 2 mean-field theory predicts that the total particle density decays as n(t) ~ 1/t, provided the system remains spatially uniform. We determine the conditions on the matrix k under which there exists a critical segregation dimension d_{seg} below which this uniformity condition is violated; the symmetry between the species is then locally broken. We argue that in those cases the density decay slows down to n(t) ~ t^{-d/d_{seg}} for 2 < d < d_{seg}. We show that when d_{seg} exists, its value can be expressed in terms of the ratio of the smallest to the largest eigenvalue of k. The existence of a conservation law (as in the special two-species annihilation A + B -> 0), although sufficient for segregation, is shown not to be a necessary condition for this phenomenon to occur. We work out specific examples and present Monte Carlo simulations compatible with our analytical results.

latex, 19 pages, 3 eps figures included

References in corpus (13)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains
• Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies
• Multi-species pair annihilation reactions
• Comment on Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• The A+B -> 0 annihilation reaction in a quenched random velocity field
• Finite Size Fluctuations in Interacting Particle Systems
• Segregation in diffusion-limited multispecies pair annihilation
• Large-Scale Simulations of Diffusion-Limited n-Species Annihilation

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