Single Particle Motions in Liquids: Qualitative Features of Memory Functions

Memory functions, which enter into the equations of motion for time correlation functions, are constructed from neutron scattering, infrared absorption and light scattering data involving single particle motions in liquids. The qualitative features of these memory functions are related to the shape of the corresponding time correlation functions. It is found that a negative portion to the memory function is indicative of a rapid loss of correlation in time while strong temporal correlations imply a memory function which does not go negative. The mathematical structure of a memory function is examined for the case of the ideal gas by expanding and evaluating the projection operator representation of the function. The resulting expression has a rich mathematical structure and can be expressed in a closed form only for its Laplace transform.