Exponents appearing in heterogeneous reaction-diffusion models in one dimension.

We study the following 1D two-species reaction diffusion model : there is a small concentration of B-particles with diffusion constant DB in an homogenous background of W-particles with diffusion constant DW ; two Wparticles of the majority species either coagulate (W + W −→ W ) or annihilate (W +W −→ ∅) with the respective probabilities pc = (q − 2)/(q − 1) and pa = 1/(q − 1); a B-particle and a W-particle annihilate (W + B −→ ∅) with probability 1. The exponent θ (q, λ = DB/DW ) describing the asymptotic time decay of the minority B-species concentration can be viewed as a generalization of the exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D q-state Potts model starting from a random initial condition : the W-particles represent domain walls, and the exponent θ(q, λ) characterizes the time decay of the probability that a diffusive “spectator” does not meet a domain wall up to time t. We extend the methods introduced by Derrida, Hakim and Pasquier (Phys. Rev. Lett. 75 751 (1995); Saclay preprint T96/013, to appear in J. Stat. Phys. (1996)) for the problem of persistent spins, to compute the exponent θ(q, λ) in perturbation at first order in (q − 1) for arbitrary λ and at first order in λ for arbitrary q. 05.40.+j, 02.50.-r, 82.20.-w Typeset using REVTEX 1