Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction

Abstract

The $A+B\to 0$ diffusion-limited reaction, with equal initial densities $a(0)=b(0)=n_0$, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension $d>2$ an effective theory is derived, from which the density and correlation functions can be calculated. We find the density decays in time as $a,b \sim C\sqrt{\D}(Dt)^{-d/4}$ for $d<4$, with $\D = n_0-C^\prime n_0^{d/2} + \dots$, where $C$ is a universal constant, and $C^{\prime }$ is non-universal. The calculation is extended to the case of unequal diffusion constants $D_A\ne D_B$, resulting in a new amplitude but the same exponent. For $d\le 2$ a controlled calculation is not possible, but a heuristic argument is presented that the results above give at least the leading term in an $\epsilon =2-d$ expansion. Finally, we address reaction zones formed in the steady-state by opposing currents of $A$ and $B$ particles, and derive scaling properties.

17 pages, REVTeX, 13 compressed figures, included with epsf. Eq. (6.12) corrected, and a moderate rewriting of the introduction. Accepted for publication in J. Stat. Phys

References in corpus (3)

• Renormalization Group Calculation for the Reaction $kA\to \varnothing$
• Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
• Possibilities and Limitations of Gaussian Closure Approximations for Phase Ordering Dynamics

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