Noise-induced clumping in the one-dimensional reversible diffusion-limited single-species coagulation process

Abstract

We investigate the interplay of internal fluctuations and external noise in the diffusion-reaction system A+A↔A, where the coagulation reaction is in the diffusion-controlled regime. Our theoretical treatment of the system is based on a recently developed exact and unified description that accounts for both types of random fluctuations. Specifically, we study the case where the external noise affects the diffusion coefficient, i.e., the coagulation rate, and is given by a dichotomous Markov process. We provide exact solutions for the steady state of the system and show that the spatially homogeneous external noise drives the system out of thermodynamic equilibrium. The noise induces microscopic spatial correlations between the particle positions. We compare this noiseinduced clumping to the previously studied case of external noise in the birth rate, and discuss the similarities and differences.