Renormalization group study of the A+B→{circled division slash} diffusion-limited reaction

Journal article

The A+B→{circled division slash} diffusion-limited reaction, with equal initial densities a(0)=b(0)=n0, 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 call be calculated. We find the density decays in time as {Mathematical expression} for d<4, with Δ=n0-C′n0d/2+..., where C is a universal constant and C′ is nonuniversal. The calculation is extended to the case of unequal diffusion constants DA≠DB, resulting in a new amplitude but the same exponent. For d≤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 ε=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. © 1995 Plenum Publishing Corporation.

Authors: Lee, B; Cardy, J

• Publisher: Kluwer Academic Publishers-Plenum Publishers
• Journal: Journal of Statistical Physics
• Volume: 80
• Issue: 5-6
• Pages: 971-1007
• Publication date: 1995-09-01
• DOI: 10.1007/BF02179861
• EISSN: 1572-9613
• ISSN: 0022-4715
• Language: English
• Keywords: asymptotic densities; Diffusion-limited reaction; renormalization group