Abstract
We present the exact dynamics of a diffusing probability distribution in a coupled two-state system. The motion of the distribution is governed by coupled Smoluchowski equations. We propose a time-domain method which is exactly analytical and can be applied to arbitrary initial probability distribution. In this paper, the method is applied to the case of Gaussian initial condition and when the coupling function is a finite strength Dirac delta function. The two potential curves are assumed to be flat. The exact analytical expressions for probability distribution are presented which are usually evaluated numerically. We verify our results numerically.
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