MICROSCOPIC SPATIAL CORRELATIONS INDUCED BY EXTERNAL NOISE IN A REACTION DIFFUSION SYSTEM

The reversible single species reaction scheme X <-- --> 2X has long served as an example of a system with nonlinear macroscopic dynamics. In recent years a microscopic version of this interacting particle system, namely the diffusion-controlled limit, has been solved exactly in one spatial dimension. The effects of internal fluctuations, correlations arising in nonequilibrium situations, and external noise can all be studied in this model diffusion-reaction system without approximation. Here we review some recent results, focusing on an exact treatment of the effect of spatially homogeneous temporal fluctuations in the growth rate of the process (the rate for the X --> 2X process). We find that the nonequilibrium steady state possesses new microscopic length scales resulting from the nonequilibrium constraints, demonstrating that spatially homogeneous external noise can introduce spatial correlations.