Spatial Organization in the Reaction A + B --> inert for Particles with a Drift

TL;DR

This paper analyzes the spatial structure of particles in a one-dimensional two-species annihilation reaction with drift, revealing distinct long-time length scales for particle arrangements compared to non-drift cases.

Contribution

It introduces a detailed analysis of spatial organization and identifies new length scales in the reaction with drift, extending understanding beyond previous models without drift.

Findings

Three relevant length scales at long times: between similar particles, between dissimilar particles, and cluster size.

Length scales differ from those in non-drift particle systems.

The analysis provides insight into the spatial dynamics of drift-influenced annihilation reactions.

Abstract

We describe the spatial structure of particles in the (one dimensional) two-species annihilation reaction A + B --> 0, where both species have a uniform drift in the same direction and like species have a hard core exclusion. For the case of equal initial concentration, at long times, there are three relevant length scales: the typical distance between similar (neighboring) particles, the typical distance between dissimilar (neighboring) particles, and the typical size of a cluster of one type of particles. These length scales are found to be generically different than that found for particles without a drift.