Corrections to reaction-diffusion dynamics above the upper critical dimension

Abstract

Reaction-diffusion models are common in many areas of statistical physics, where they describe the late-time dynamics of chemical reactions. Using a Bose gas representation, which maps the real-time dynamics of the reactants to the imaginary-time evolution of an interacting Bose gas, we consider corrections to the late-time scaling of $k$-particle annihilation processes $kA\to \varnothing$ above the upper critical dimension, where mean-field theory sets the leading order. We establish that the leading corrections are not given by a small renormalization of the reaction rate due to $k$-particle memory effects, but instead set by higher-order correlation functions that capture memory effects of sub-clusters of reactants. Drawing on methods developed for ultracold quantum gases and nuclear physics, we compute these corrections exactly for various annihilation processes with $k>2$.

11 pages, 7 figures

References in corpus (4)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• Scattering Models for Ultracold Atoms
• Universal Scaling Laws in the Dynamics of a Homogeneous Unitary Bose Gas

Cited by in corpus (1)

• Scaling Laws Governing the Collapse of a Bose-Einstein Condensate