Conserved quantities and the effect of external input on the decay of density fluctuations in steady state reaction–diffusion systems

Abstract

Using the fluctuation dissipation theory developed by Keizer a study is made of the long-time asymptotics of the particle number correlation function, Gij(r,t)=〈δρi(r,t)δρj(0,0)〉 (i,j=A,B), for steady states of diffusion mediated reactions with external random input. For the reaction A+B→P we find a power decay, Gij(r,t)∝t−ν, with the exponent ν whose value depends on the type of input and the dimensionality of the system d. In the case of an uncorrelated input ν=1/2 in three spatial dimensions. When particles are added locally in pairs ν=d/2. For the reaction 2A→P the correlation function decays exponentially fast. These results are discussed in terms of the existence of a quantity which is conserved by the reaction and the stochastic properties of the input process.