Continued-Fraction Description of Collective Motion in Simple Fluids

Abstract

In this paper a many-variable form of the Mori continued-fraction technique is employed to investigate the relaxation function of simple liquids. A general relationship between a truncated-continued-fraction expression and the Zwanzig and Nossal variational result for the relaxation function is presented. In addition, a specific example of this relationship is explored to show the connection between the eigenvalues found from high-frequency hydrodynamic equations and those obtained from a variational method. The structure of the relaxation function in the low-wave-vector limit is examined in considerable detail, and some comments are made concerning the applicability of the variational method in the low-wave-vector and high-frequency regime.