Fluctuations in reaction-diffusion systems: a new exactly soluble growth model

The method of compounding moments devised by Van Kampen is used to study the spatial fluctuations in a model describing the irreversible formation of clusters. The reaction and diffusion constants in this model are chosen independent of the cluster sizes. For a monodisperse initial distribution explicit expressions are calculated for the equal-time and two-time correlation functions of the concentrations of m- and n-mers. For general initial conditions the fluctuations in the mass density are considered and a scaling theory is presented for the fluctuations at large times. Extensions to more general models are discussed