Hydrodynamic dispersion relations in dense fluids

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Abstract
Concepts of hydrodynamics and hydrodynamic modes are explored for dense fluids under conditions for which mode-coupling effects are important. Dispersion relations associated with the matrix of equilibrium time correlation functions for conserved densities are studied to isolate the hydrodynamic part of its spectrum. An Enskog-like model for hard spheres, including lowest-order bilinear density mode-coupling effects, is used for the analysis over a wide range of dense fluid conditions and for wavelengths extending down to those of the order of the correlation length. The hydrodynamic branch is identified as that which vanishes in the long-wavelength limit. The dispersion relations are investigated to determine the existence of such a hydrodynamic spectrum, and its possible extension to short wavelengths. Mode-coupling effects are shown to complicate the usual simple pole structure by introducing branch points that also vanish in the long-wavelength limit. Emphasis of this study is placed on the mode corresponding to heat diffusion. It is found that mode-coupling effects introduce significant changes in the extended modes, but the soft heat mode at wavelengths of the order of the correlation length remains a simple pole and provides the dominant contribution to the density autocorrelation function.