Effective rate equations for the overdamped motion in fluctuating potentials.
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 fluctuations 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. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.
Mielke
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Institut für Theoretische Physik, Ruprecht Karls Universität, Philosophenweg 19, D-69120 Heidelberg, Germany.