Two-Species Annihilation with Drift: A Model with Continuous Concentration-Decay Exponents

TL;DR

This paper introduces a model for two-species annihilation with drift, showing that the decay exponent varies continuously with reaction probabilities, indicating a lack of universal behavior in such diffusion-limited reactions.

Contribution

The study presents a novel model demonstrating continuous variation of decay exponents in diffusion-limited annihilation with drift, challenging the notion of universal classes.

Findings

Decay follows a power-law at large times.

Decay exponent varies continuously with reaction probabilities.

Reveals non-universality in diffusion-limited reactions with drift.

Abstract

We propose a model for diffusion-limited annihilation of two species, $A+B\to A$ or $B$, where the motion of the particles is subject to a drift. For equal initial concentrations of the two species, the density follows a power-law decay for large times. However, the decay exponent varies continuously as a function of the probability of which particle, the hopping one or the target, survives in the reaction. These results suggest that diffusion-limited reactions subject to drift do not fall into a limited number of universality classes.