Two-Species Reaction-Diffusion System with Equal Diffusion Constants: Anomalous Density Decay at Large Times

TL;DR

This paper investigates a two-species reaction-diffusion system with equal diffusion constants, revealing that the minority species decays at the same rate as the majority in low dimensions, supported by theoretical and numerical analysis.

Contribution

It provides a field-theoretic analysis and Monte Carlo simulations showing anomalous density decay behavior in a two-species reaction-diffusion system with equal diffusion constants.

Findings

Minority species decay rate matches majority in d<=2.

Field theory predicts equal decay rates for both species.

Monte Carlo simulations support theoretical predictions in d=1.

Abstract

We study a two-species reaction-diffusion model where A+A->0, A+B->0 and B+B->0, with annihilation rates lambda0, delta0 > lambda0 and lambda0, respectively. The initial particle configuration is taken to be randomly mixed with mean densities nA(0) > nB(0), and with the two species A and B diffusing with the same diffusion constant. A field-theoretic renormalization group analysis suggests that, contrary to expectation, the large-time density of the minority species decays at the same rate as the majority when d<=2. Monte Carlo data supports the field theory prediction in d=1, while in d=2 the logarithmically slow convergence to the large-time asymptotics makes a numerical test difficult.