Combined effect of periodic gates and external fields on the diffusion coefficient of a single particle

A general analytical expression to describe the diffusion of a single particle in a one-dimensional lattice with periodically distributed gates of lifetime (tau) and while under the influence of a constant external field is calculated. A formulation based on a microscopic model and a diffusion relaxation condition is used to derive an equation for the diffusion coefficient as a function of the concentration of gates (c), the lifetime (tau) of such gates, and the strength of the external field (p). The theory is compared against Monte Carlo simulations, and limiting cases are used to reproduce previously published results on a variety of phenomena.