  The velocity auto-correlation spectra of simple liquids obtained by the NMR
method of modulated gradient spin echo show features in the low frequency range
up to a few kHz, which can be explained reasonably well by a $t^{-3/2}$ long
time tail decay only for non-polar liquid toluene, while the spectra of polar
liquids, such as ethanol, water and glycerol, are more congruent with the model
of diffusion of particles temporarily trapped in potential wells created by
their neighbors. As the method provides the spectrum averaged over ensemble of
particle trajectories, the initial non-exponential decay of spin echoes is
attributed to a spatial heterogeneity of molecular motion in a bulk of liquid,
reflected in distribution of the echo decays for short trajectories. While at
longer time intervals, and thus with longer trajectories, heterogeneity is
averaged out, giving rise to a spectrum which is explained as a combination of
molecular self-diffusion and eddy diffusion within the vortexes of hydrodynamic
fluctuations.
