Collective Dynamics of Glass-Forming Liquids in Two and Three Dimensions*

We evaluate the collective density-density and hydrostatic pressure-pressure correlations in two- and three-dimensional single-component coarse-grained polymer melts and binary Lennard-Jones liquids over a wide range of time and length scales using molecular dynamics simulations. At temperatures above the dynamic crossover, the mesoscopic collective dynamics in three-dimensional simulations can be qualitatively understood with the classical hydrodynamic theory. At lower temperatures, wavenumber-independent non-hydrodynamic modes emerge at long times. Such a connection between dynamic crossover and mesoscopic collective dynamics in 3D simualtions is critically tested in 2D systems and the results will be discussed in this talk.