Abstract
The motion of particles in modulated potentials is studied, starting from a Smoluchowski equation for the evolution of the probability distribution function. A general method to solve this explicitely time dependent Smoluchowski equation is presented and applied to the case of particles in time dependent double well potentials.
For special kinds of time dependence (modulation of the barrier between the wells, modulation of the energy difference between the bottoms of the wells, modulated dilatation) the probability distribution function as well as the occupation probabilities of the two wells and the related time dependent transition probabilities are explicitely given and discussed.
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Bunde, A., Gouyet, J.F. Diffusion in time dependent potentials: A systematic treatment. Z. Physik B - Condensed Matter 42, 169–181 (1981). https://doi.org/10.1007/BF01319552
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DOI: https://doi.org/10.1007/BF01319552