Kinetics of Heterogeneous Single-Species Annihilation

TL;DR

This paper studies how different diffusion rates affect the kinetics of single-species annihilation, revealing non-universal decay behaviors and providing theoretical and simulation validation across dimensions.

Contribution

It introduces a comprehensive analysis of heterogeneous diffusion-controlled annihilation, deriving decay exponents for various diffusivity ratios using mean-field and Smoluchowski theories.

Findings

Concentration decay of least mobile species matches homogeneous case.

More mobile species decay with non-universal power laws.

Theoretical predictions align well with simulations and series expansions.

Abstract

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A-->0. However, the concentrations of more mobile species decay as power laws in time, but with non-universal exponents that depend on the ratios of the corresponding diffusivities to that of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimension d>2, and in a phenomenological Smoluchowski theory which is applicable in d<2. Our theoretical predictions compare well with both Monte Carlo simulations and with time series expansions.