Three-Species Diffusion-Limited Reaction with Continuous Density-Decay Exponents

TL;DR

This paper investigates a three-species diffusion-limited reaction model in one dimension, analyzing how particle density decay varies with parameters and diffusion anisotropy, revealing complex behavior and challenging existing universality class assumptions.

Contribution

It introduces a novel three-species reaction model with persistence parameters and explores its decay dynamics under isotropic and anisotropic diffusion in one dimension.

Findings

Particle density exhibits power-law decay for specific parameter values.

Decay exponents vary continuously with parameters in anisotropic diffusion.

Most parameter choices do not produce power-law decay, indicating complex universality behavior.

Abstract

We introduce a model of three-species two-particle diffusion-limited reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three persistence parameters (survival probabilities in reaction) of the hopping particle. We consider isotropic and anisotropic diffusion (hopping with a drift) in 1d. We find that the particle density decays as a power-law for certain choices of the persistence parameter values. In the anisotropic case, on one symmetric line in the parameter space, the decay exponent is monotonically varying between the values close to 1/3 and 1/2. On another, less symmetric line, the exponent is constant. For most parameter values, the density does not follow a power-law. We also calculated various characteristic exponents for the distance of nearest particles and domain structure. Our results support the recently proposed possibility that 1d diffusion-limited reactions with a drift do not fall within a limited number of distinct universality classes.