Reaction diffusion models in one dimension with disorder

We study a large class of one-dimensional reaction diffusion models with qu enched disorder using a real space renormalization group method (RSRG) whic h yields exact results at large time. Particles (e.g., of several species) undergo diffusion with random local bias (Sinai model) and may react upon m eeting. We obtain a detailed description of the asymptotic states (i.e., at tractive fixed points of the RSRG), such as the large time decay of the den sity of each specie, their associated universal amplitudes, and the spatial distribution of particles. We also derive the spectrum of nontrivial expon ents which characterize the convergence towards the asymptotic states. For reactions which lead to several possible asymptotic states separated by uns table fixed points, we analyze the dynamical phase diagram and obtain the c ritical exponents characterizing the transitions. We also obtain a detailed characterization of the persistence properties for single particles as wel l as more complex patterns. We compute the decay exponents for the probabil ity of no crossing of a given point by, respectively, the single particle t rajectories (theta) or the thermally averaged packets (<(theta)over bar>). The generalized persistence exponents associated to ii crossings are also o btained. Specifying to the process A + A--> phi or A with probabilities (I, 1-r), we compute exactly the exponents delta(A)(r) and psi(r) characterizin g the survival up to time t of a domain without any merging or with merging s, respectively, and the exponents delta(A)(r) and psi(A)(r) characterizing the survival up to time t of a particle A without any coalescence or with coalescences, respectively. <(theta)over bar>, psi and delta obey hypergeom etric equations and are numerically surprisingly close to pure system expon ents (though associated to a completely different diffusion length). The ef fect of additional disorder in the reaction rates, as well as some open que stions, are also discussed. [S1063-651X(99) 15005-0].