High-Frequency Expansion of Memory Function in Classical Simple Liquids

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Abstract
Elementary excitations in classical simple liquids are studied by employing a high-frequency expansion of a memory function in the generalized Langevin equation for the density fluctuations. Explicit expressions for the first four expansion terms are obtained that ensure the correct zeroth, second, fourth and sixth frequency moments of a dynamic structure factor S(k,ω). Numerical calculations of dispersion curves of elementary excitations are made for liquid argon with particular attention paid to the region in the vicinity of the first peak in the structure factor. Good agreement with experimental data both from computer simulations and from neutron scattering measurements are obtained, provided an approximate cancellation is assumed to take place between a term containing a three-body correlation function and terms with a two-body correlation function which appears in an expansion term giving the sixth frequency moment of S(k,ω). This result, combined with a more careful analysis of the sixth and higer frequency moments of S(k,ω), may elucidate the role of the three-body correlation function in determining the dispersion of elementary excitations in classical simple liquids.

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