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

I. M. Sokolov, S. B. Yuste, J. J. Ruiz-Lorenzo, Katja Lindenberg

Published 2008-11-25, updated 2009-02-16Version 3

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.