  Investigating million-atom systems for very long simulation times, we
demonstrate that the collective density-density correlation time
($\tau_{\alpha}$) in simulated supercooled water and silica becomes wavevector
independent ($q^0$) when the probing wavelength is several times larger than
the interparticle distance. The $q$-independence of the collective
density-density correlation functions, a feature clearly observed in
light-scattering studies of some soft-matter systems, is thus a genuine feature
of many (but not all) slow-dynamics systems, either atomic, molecular or
colloidal. Indeed, we show that when the dynamics of the density fluctuations
is due to particle-type diffusion, as in the case of the Lennard Jones binary
mixture model, the $q^0$ regime does not set in and the relaxation time
continues to scale as $\tau_{\alpha} \sim q^{-2}$ even at small $q$.
