Collective acoustic modes in liquids: a comparison between the generalized-hydrodynamics and memory-function approaches

The most familiar approaches used to describe the dynamical structure factor from adiabatic density fluctuations in liquids are based on generalized hydrodynamics and on the memory function, respectively. We show that, contrary to the common belief, the two approaches are not fully equivalent. In particular, models based on the memory function of a normalized damped oscillator fail in reproducing the correct experimental spectral profiles of systems close to the relaxation process. The discrepancy is due to misleading interpretation of the theoretical memory-function expressions, producing an unavoidable mixing of spectral contribution at different wave vectors when the theory is forced beyond its limits of validity.