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Analytical study of a flashing molecular pump

We present a model for a molecular pump of neutral particles which is powered by a flashing ratchet mechanism. This device obeys a Langevin equation with multiplicative noise and it is embedded in a cell membrane bounded by two particle reservoirs. Thus, and unlike typical Brownian motors, the boundary conditions are not periodic nor the normalization condition is imposed. Instead, we study the steady state either at zero or finite flux and derive an exact solution for the density profile of particles. The ratio of concentrations created at both ends of the system and the flux are explored as a function of the parameters of the model.