Effects of intrinsic noise on a cubic autocatalytic reaction-diffusion system.

Abstract

Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions U+2V→[over λ_{0}]3V and V→[over μ]P, U→[over ν]Q, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces n→n molecular interaction processes with n≥4, where n is the number of participating molecules of type U or V. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state σ=ϕ_{u}ϕ_{v}^{2}, where ϕ_{i} corresponds to the fields representing the densities of U and V. Finally, we discuss the difference between representing σ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension, we find that while they show markedly different behavior in the short spatiotemporal scale, high-momentum (UV) limit, they are formally equivalent in the large spatiotemporal scale, low momentum (IR) regime. On the other hand, in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite σ. Thus, in this regime, σ behaves as an entity unto itself, suggesting that it can be effectively treated as an independent chemical species.