Reaction rate in an evanescent random walkers system

TL;DR

This paper develops an analytical model for reaction rates involving evanescent random walkers in one-dimensional diffusion, accounting for finite absorption rates and analyzing both short and long time behaviors.

Contribution

It introduces a new diffusion-limited reaction model with evanescent walkers, providing analytical expressions for absorption probability and reaction rate in Laplace space.

Findings

Analytical expressions for absorption probability density.

Reaction rate behavior at short and long times.

Impact of finite absorption rate on reaction dynamics.

Abstract

Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models have received attention in order to include finite lifetime processes. For instance, activated chemical reactions, such as laser photolysis, exhibit a different asymptotic limit when compared with immortal walker models. A diffusion limited reaction model based on a one dimensional continuous time random walk on a lattice with evanescent walkers is presented here. The absorption probability density and the reaction rate are analytically calculated in the Laplace domain. A finite absorption rate is considered, a model usually referred to as imperfect trapping. Short and long time behaviors are analyzed.