Mean Field Model of Coagulation and Annihilation Reactions in a Medium of Quenched Traps: Subdiffusion

TL;DR

This paper develops a mean field model for coagulation and annihilation reactions in a trap-lattice system with a power-law distribution of trap depths, examining how reactions influence aging and particle distribution over time.

Contribution

It introduces a novel mean field framework incorporating trap depth distributions and explores reaction effects on aging phenomena in subdiffusive media.

Findings

Reactions modify the aging behavior of particle distributions.

The model captures subdiffusive dynamics due to trap depth heterogeneity.

Reactions influence the evolution of particle concentration over time.

Abstract

We present a mean field model for coagulation ($A+A\to A$) and annihilation ($A+A\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is exponentially distributed about the mean for that trap, and the distribution of mean escape times is a power law. Even in the absence of reactions, the distribution of particles over sites changes with time as particles are caught in ever deeper traps, that is, the distribution exhibits aging. Our main goal is to explore whether the reactions lead to further (time dependent) changes in this distribution.