Dissipative dynamics of a harmonic oscillator with environmentally caused frequency modulation

Abstract

The primary objective of the present work is an exact theoretical analysis of a vibrational dephasing process. We have investigated a microscopic counterpart of the well known stochastic model of random harmonic oscillator frequency modulation. We have found an exact expression for the oscillator coordinate relaxation. Several principal features of our solution appear to be quite different from the results based on the random frequency modulation model. (i) The envelope function of the oscillator coordinate time dependence is a function of temperature and it reveals definite types of coherent beats. (ii) The 'frequency' of the coordinate oscillations is time dependent and exhibits definite shift relative to the bare oscillator frequency when time goes from zero to infinity. (iii) Both the envelope function and the 'frequency' of the coordinate oscillations depend on the initial oscillator energy. This demonstrates the interaction-introduced non-linearity of the resulting dynamics.