Formal Solution of a Class of Reaction-Diffusion Models: Reduction to a Single-Particle Problem

TL;DR

This paper presents a formal method to analyze a class of reaction-diffusion models by reducing the problem to a single-particle dynamics, enabling calculation of survival probabilities and spatial statistics.

Contribution

It introduces a novel formal reduction technique for reaction-diffusion models, applicable to trapping and annihilation reactions in low dimensions.

Findings

Derived an effective single-particle dynamics for A particles

Calculated survival probabilities and spatial fluctuations

Extended method to other reaction types in two dimensions

Abstract

We consider the trapping reaction A + B -> B in space dimension d<=2. By formally eliminating the B particles from the problem we derive an effective dynamics for the A particles from which the survival probability of a given A particle and the statistics of its spatial fluctuations can be calculated in a rather general way. The method can be extended to the study of annihilation/coalescence reactions, B + B -> 0 or B, in d=2.