Corrections to reaction-diffusion dynamics above the upper critical dimension

TL;DR

This paper investigates corrections to the late-time behavior of reaction-diffusion systems above the upper critical dimension, revealing that higher-order correlations, rather than simple rate renormalizations, dominate these corrections.

Contribution

It introduces a novel approach using Bose gas representation to compute exact corrections from higher-order correlations in reaction-diffusion models.

Findings

Corrections are governed by higher-order correlation functions.

Exact calculations performed for processes with k>2.

Memory effects of sub-clusters are crucial for accurate modeling.

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 $k A \to \emptyset$ 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 $k>2$.