'Real' versus 'imaginary' noise in diffusion-limited reactions

Abstract

Reaction-diffusion systems which include processes of the form A+A → A or A + A → ∅ are characterized by the appearance of ‘imaginary’ multiplicative noise terms in an effective Langevin-type description. However, if ‘real’ as well as ‘imaginary’ noise is present, then competition between the two could potentially lead to novel behavior. We thus investigate the asymptotic properties of the following two ‘mixed noise’ reaction-diffusion systems. The first is a combination of the annihilation and scattering processes 2A → ∅, 2A → 2B, 2B → 2A, and 2B → ∅. We demonstrate (to all orders in perturbation theory) that this system belongs to the same universality class as the single species annihilation reaction 2A → ∅. Our second system consists of competing annihilation and fission processes, 2A → ∅ and 2A → (n + 2)A, a model which exhibits a transition between active and absorbing phases. However, this transition and the active phase are not accessible to perturbative methods, as the field theory describing these reactions is shown to be non-renormalizable. This corresponds to the fact that there is no stationary state in the active phase, where the particle density diverges at finite times. We discuss the implications of our analysis for a recent study of another active / absorbing transition in a system with multiplicative noise.