EXPONENTS APPEARING IN HETEROGENEOUS REACTION-DIFFUSION MODELS IN ONE-DIMENSION

We study the following one-dimensional (1D) two-species reaction-diffu sion model: there is a small concentration of B particles with diffusi on constant D-B in an homogenous background of W particles with diffus ion constant D-W; two W particles of the majority species either coagu late (W+W-->W) or annihilate (W+W-->0) with the respective probabiliti es p(c)=(q-2)/(q-1) and p(a)=1/(q-1); a B particle and a W particle an nihilate (W+B-->0) with probability 1. The exponent theta(q,lambda=D-g /D-W) describing the asymptotic time decay of the minority B species c oncentration can be viewed as a generalization of the exponent of pers istent spins in the zero-temperature Glauber dynamics of the 1D q-stat e Potts model starting from a random initial condition: the W particle s represent domain walls, and the exponent theta(q,lambda) characteriz es the time decay of the probability that a diffusive ''spectator'' do es not meet a domain wall up to time t. We extend the methods introduc ed 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 theta(q,lambda) in perturbation at first order in (q-1) for arbitrary lambda and at first order in lambda for arbitr ary q.