Non-nearest neighbor random walks in reaction-diffusion processes

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Abstract
In this paper, we consider reaction-diffusion processes in which it is assumed that a migrating species (A) is subject to an interaction potential and may undertake nonnearest neighbor jumps in its diffusion towards a reaction center (B). For the case that the species A and B react irreversibly upon first encounter, we show how the efficiency of the process A+B → C is influenced by the nature of the interaction potential [a power law of the form V (r) =r−s with r≳0 and 1≤s≤12] and the geometry (dimensionality and spatial extent) of the reaction space assumed. Our approach is based on a recently introduced, exact theory of d-dimensional walks on finite and infinite (periodic) lattices with traps and, accordingly, the results presented in this study provide an exact quantitation of the interplay between potential interactions and system geometry for the reaction-diffusion problems considered. The results reported here may have considerable relevance to the problems of exciton migration in crystals, photosynthesis, and the surface diffusion of adatoms.