Dynamics in condensed phase for systems involving phase functions obeying Gaussian statistics

Abstract

The study of non-equilibrium processes in condensed phase has been fascinating and has attracted considerable attention of experimentalists as well as theoreticians during the last few decades. Since the theoretical treatment using Liouville equation involves multi-dimensional phase space functions, it is very difficult to visualize and also to obtain analytical expressions for the time-dependent distribution functions in Liouville space, which has led to formulation of various reduced space descriptions. The bottleneck in describing the non-equilibrium processes in the reduced space lies in the appearance of coupled velocity and position correlation functions in the equations, which are difficult to evaluate in general. In this work, we have developed a scheme to decouple the complicated multi-point coupled correlation function into two-point velocity and position correlation functions for situations characterized by a time-dependent phase function obeying Gaussian distribution, by making use of the Novikov's theorem. As an illustrative application, we have investigated the problem of optically controlled solvation dynamics and obtained exact expressions for the non-equilibrium solvation time correlation functions showing explicit dependence on the excitation frequency, as observed experimentally. We have shown that the linear response theory result is valid as long as the energy gap obeys the Gaussian distribution, rescuing the linear response theory based result from the domain of validity for small fluctuations in solvation coordinate.