q-Independent Slow Dynamics in Atomic and Molecular Systems

Investigating million-atom systems for very long simulation times, we demonstrate that the collective density-density correlation time (τ_α) in simulated supercooled water and silica becomes wave-vector 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 includes 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 τ_α∼q^-2 even at small q