Abstract
TheA+B→⊘ diffusion-limited reaction, with equal initial densitiesa(0)=b(0)=n 0, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimensiond>2 an effective theory is derived, from which the density and correlation functions call be calculated. We find the density decays in time as\(a,b \sim C\sqrt \Delta (Dt)^{ - d/4} \) ford<4, with Δ=n 0 −C′n d/20 +..., whereC is a universal constant andC′ is nonuniversal. The calculation is extended to the case of unequal diffusion constantsD A ≠D B , resulting in a new amplitude but the same exponent. Ford⩽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 ofA andB particles, and derive scaling properties.
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Lee, B.P., Cardy, J. Renormalization group study of theA+B→⊘ diffusion-limited reaction. J Stat Phys 80, 971–1007 (1995). https://doi.org/10.1007/BF02179861
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DOI: https://doi.org/10.1007/BF02179861