Localized partial traps in diffusion processes and random walks

Reaction-diffusion equations, in which the reaction is described by a sink term consisting of a sum of delta functions, are studied. It is shown that the Laplace transform of the reactive Green's function can be analytically expressed in terms of the Green's function for diffusion in the absence of reaction. Moreover, a simple relation between the Green's functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained. Several applications are presented and the formalism is used to establish the relationship between the time-dependent geminate recombination yield and the bimolecular reaction rate for diffusion-influenced reactions. Finally, an analogous development for lattice random walks is presented.