Localisation Transition of A Dynamic Reaction Front

TL;DR

This paper investigates a reaction-diffusion system with opposing boundary injections and bulk driving, revealing phase transitions between localized and delocalized reaction zones, and provides an analytical phase diagram relating to asymmetric exclusion processes.

Contribution

It introduces a novel reaction-diffusion model with boundary-driven reactions and derives an approximate analytical phase diagram based on asymmetric exclusion processes.

Findings

Identification of phase transitions between localised and delocalised reaction zones.

Derivation of an approximate analytical phase diagram.

Distinct scaling exponents for reaction zone width in different phases.

Abstract

We study the reaction-diffusion process $A+B\to \emptyset$ with injection of each species at opposite boundaries of a one-dimensional lattice and bulk driving of each species in opposing directions with a hardcore interaction. The system shows the novel feature of phase transitions between localised and delocalised reaction zones as the injection rate or reaction rate is varied. An approximate analytical form for the phase diagram is derived by relating both the domain of reactants $A$ and the domain of reactants $B$ to asymmetric exclusion processes with open boundaries, a system for which the phase diagram is known exactly, giving rise to three phases. The reaction zone width $w$ is described by a finite size scaling form relating the early time growth, relaxation time and saturation width exponents. In each phase the exponents are distinct from the previously studied case where the reactants diffuse isotropically.