The A+B→0 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 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′ is non-universal. 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.Comment: 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. Phy