Analytical representation of time correlation functions and application to relaxation problems

Two analytical representations of the Laplace transform of the time autocorrelation of a dynamical variable, namely the moment expansion and Mori's continued fraction expansion, are investigated from the point of view of structure and convergence properties, and the relation between them is established. The general theory is applied first to a dynamical model exactly solvable, the isotopic impurity in a linear chain of coupled harmonic oscillators, and then to two stochastic models recently introduced by Gordon for the rotational diffusion of molecules. In the latter case, the continued fraction expansion yields simple analytical expressions for the infrared absorption band shapes, showing that these models contain all the features of observed shapes in compressed gases, liquids and solutions. (author)