Abstract
We study kinetics of single-species reactions ("A + A → ∅") for general local reactivity Q and dynamical exponent z (rms displacement xt ∼ t1/z.) For small molecules z = 2, whilst z = 4,8 for certain polymer systems. For dimensions d above the critical value dc = z, kinetics are always mean field (MF). Below dc, the density nt initially follows MF decay, n0 − nt ∼ n02Qt. A 2-body diffusion-controlled regime follows for strongly reactive systems (Q > Q* ∼ n0(z − d)/d) with n0 − nt ≈ n02xtd. For Q < Q*, MF kinetics persist, with nt ∼ 1/Qt. In all cases nt ≈ 1/xtd at the longest times. Our analysis avoids decoupling approximations by instead postulating weak physically motivated bounds on correlation functions.