Effective rate equations for the over-damped motion in fluctuating potentials

Details Effective rate equations for the over-damped motion in fluctuating potentials Effective rate equations for the over-damped motion in fluctuating potentials

2001-04-18

arxiv.org/abs/cond-mat/0104330v1

Phys. Rev. E64, 021106, 1-12 (2001)

Physics

Condensed Matter

Statistical Mechanics

18 pages, 2 figures, standard LaTeX2e

Scientific paper

10.1103/PhysRevE.64.021106

We discuss physical and mathematical aspects of the over-damped 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.

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