Anomalous Dimension in a Two-Species Reaction-Diffusion System

Abstract

We study a two-species reaction-diffusion system with the reactions $A+A\to (0,A)$ and $A+B\to A$, with general diffusion constants $D_A$ and $D_B$. Previous studies showed that for dimensions $d\le 2$ the $B$ particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the $B$ particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling $C_{BB}(r,t)\sim t^{\varphi }f(r/\sqrt{t})$, where the exponent $\varphi$ results from the renormalization of the square of the field associated with the $B$ particles. We compute this exponent to first order in $\epsilon =2-d$, a calculation that involves 61 Feynman diagrams, and also determine the logarithmic corrections at the upper critical dimension $d=2$. Finally, we determine the exponent $\varphi$ numerically utilizing a mapping to a four-walker problem for the special case of $A$ particle coalescence in one spatial dimension.

arXiv comment(9 pages, 7 figures, corrigendum included)

References in corpus (18)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Theory of Branching and Annihilating Random Walks
• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Field Theory of Branching and Annihilating Random Walks
• The Field Theory Approach to Percolation Processes
• Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
• Capture of the Lamb: Diffusing Predators Seeking a Diffusing Prey
• Kinetics of Heterogeneous Single-Species Annihilation
• Fluctuation Kinetics in a Multispecies Reaction-Diffusion System
• Persistence properties of a system of coagulating and annihilating random walkers
• On the trapping reaction with mobile traps
• Ordering of Random Walks: The Leader and the Laggard
• Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers
• Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation
• Ideal Polymers near Scale-Free Surfaces
• Multi-Scaling of Correlation Functions in Single Species Reaction-Diffusion Systems
• Diffusion in the Presence of Scale-Free Absorbing Boundaries

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• Numerical Simulation of the Trapping Reaction with Mobile and Reacting Traps
• Anomalous Kinetics of a Multi-Species Reaction-Diffusion System: Effect of Random Velocity Fluctuations
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations
• Approximate calculation of functional integrals arising from the operator approach
• Two-species reaction-diffusion system in the presence of random velocity fluctuations