Diffusional effects of the processes of escape from a potential well

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Abstract
In the past few years a modeling approach has been developed to account self-consistently and simultaneously both for the non-Gaussian and non-Markovian properties of liquids. This uses a nonlinear effective interaction potential between the tagged molecule and a ‘‘virtual’’ Brownian body. The theory describes, in addition, the slope of a correlation function at long times. This is an exponential distinctly slower than that expected from the value of the Debye-type diffusion coefficient. The theory also explains, self-consistently, the slowing down of velocity correlation functions from ensembles of particles whose distribution of equilibrium corresponds to that of an excited state. Previous attempts at disclosing the physical reasons behind these two phenomena have been based on perturbation techniques which can be applied only to a very restricted class of (almost Gaussian and almost Markovian) processes where both the effects are negligible. These limitations are overcome in this paper for distinctly non-Gaussian, non-Markovian processes by using the critically important result that escapes from potential wells are the reasons behind both phenomena. The excited correlation functions are driven by activated rate processes, exhibiting a dependence upon the level of excitation which has recently been recognized to be typical of pumped processes. This would make it possible, in principle, to draw from computer experiments direct information on the nature of the ‘‘virtual’’ potential itself.

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