Exponents appearing in heterogeneous reaction-diffusion models in one dimension

We study the following one-dimensional (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 W particles of the majority species either coagulate (W+W{→}W) or annihilate (W+W{→}0) with the respective probabilities pc=(q-2)/(q-1) and pₐ=1/(q-1); a B particle and a W particle annihilate (W+B{→}0) 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); J. Stat. Phys. (to be published)] 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. {} 1996 The American Physical Society.