Reaction-diffusion with a time-dependent reaction rate: the single-species diffusion-annihilation process

TL;DR

This paper investigates how a time-dependent reaction rate affects the diffusion-annihilation process, revealing a critical decay exponent that separates reaction-limited and diffusion-limited regimes, supported by scaling arguments and Monte Carlo simulations.

Contribution

It introduces a model with a time-dependent reaction rate and identifies a critical exponent that determines the regime, supported by analytical and simulation results.

Findings

Identification of a critical decay exponent omega_c(d)

Different decay behaviors in reaction-limited and diffusion-limited regimes

Validation of scaling predictions through Monte Carlo simulations

Abstract

We study the single-species diffusion-annihilation process with a time-dependent reaction rate, lambda(t)=lambda_0 t^-omega. Scaling arguments show that there is a critical value of the decay exponent omega_c(d) separating a reaction-limited regime for omega > omega_c from a diffusion-limited regime for omega < omega_c. The particle density displays a mean-field, omega-dependent, decay when the process is reaction limited whereas it behaves as for a constant reaction rate when the process is diffusion limited. These results are confirmed by Monte Carlo simulations. They allow us to discuss the scaling behaviour of coupled diffusion-annihilation processes in terms of effective time-dependent reaction rates.