Field-theoretic technique for irreversible reaction processes

TL;DR

This paper analyzes the A+A->0 reaction with random advection using field theory, calculating fixed points, decay exponents, and scaling functions to understand the system's infrared behavior and the impact of sources and sinks.

Contribution

It introduces a two-loop approximation in a double expansion to determine fixed points, decay exponents, and scaling functions for the reaction process with random advection and sources.

Findings

Identified stable fixed points and their stability regions.

Calculated decay exponents and scaling functions to second order.

Discovered two universality classes influenced by random sources and sinks.

Abstract

The single-species annihilation reaction A+A->0 is studied in the presence of random advecting field. In order to determine possible infrared behavior of the system all stable fixed points are presented to two-loop approximation in double $(\epsilon,\Delta)$ expansion with the corresponding regions of stability. The main result of this paper is the calculation of all the renormalization constants and the decay exponent to the second-order precision as well as calculation of scaling function the mean particle number to the first order. Effects of random sources and sinks on reaction kinetics in the master-equation description have been investigated in the framework of a field-theoretic model, obtained by the "second quantization" a la Doi of the corresponding master equation. It has been demonstrated that random sources and sinks have a significant effect on the asymptotic behaviour of the model and two universality classes for their description have been identified by the scaling analysis. Results are compared with the Langevin-equation description of the same process.