Fluctuation Correlations in Reaction-Diffusion Systems: Reactive Lattice Gas Automata Approach

We model reaction-diffusion systems with reactive lattice gas automata, which possess intrinsic microscopic fluctuations. We show that, within the limits of linear theory, the commonly accepted Landau equation describes correctly the measured effects of the fluctuations, as evidenced by the density autocorrelation function. We suggest that the reactive lattice gas automata constitute a powerful method for investigating reaction-diffusion systems where intrinsic fluctuations play an important role. Microscopic fluctuations in constrained systems can produce correlations which extend over distances large compared to the range of the molecular processes. These correlations play a crucial role at the mesoscopic and macroscopic levels in various situations, in particular when symmetry breaking is triggered by the destabilization of a homogeneous steady state. Space- and time-dependent structures, such as regular or irregular patterns, may then form spontaneously. It is particularly fascin...