Effective rate equations for the overdamped motion in fluctuating potentials - art. no. 021106

We discuss physical and mathematical aspects of the overdamped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluc tuations are slow compared to relaxation within the minima of the potential , and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Further more, we show the existence of a stationary solution of the Fokker-Planck e quation that describes the motion within the fluctuating potential under so me general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.