Reaction rate in an evanescent random walkers system

Abstract

Diffusion mediated reaction models are particularly ubiquitous in the description of phys-ical, chemical or biological processes. The random walk schema is a useful tool for formu-lating these models. Recently, evanescent random walk models have received attention inorder 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.