Dynamical disorder in diffusion-limited reactions

We consider a simple model of annihilation reaction, when particles are located on a regular lattice, one of them presenting a fluctuating activity. Time-correlated fluctuations are addressed. The reaction probability and the reaction function are determined exactly. It is shown that the usual, mean-field theory of chemical kinetics does not hold. In particular, the classical law of chemical kinetics does not apply in low dimensions. In three dimensions, a chemical constant exists and it increases with the relaxation frequency of the fluctuations λ. Previously known results are recovered in the limit case of uncorrelated fluctuations, when λ→∞. Different related models, which cannot be solved exactly, are discussed in this limit case