Abstract
Many systems, including polymers and molecular liquids, when adequately cooled and/or compressed, solidify into a disordered solid, i.e., a glass. The transition is not abrupt, featuring progressive decrease of the microscopic mobility and huge slowing down of the relaxation. A distinctive aspect of glass-forming materials is the microscopic dynamical heterogeneity (DH), i.e., the presence of regions with almost immobile particles coexisting with others where highly mobile ones are located. Following the first compelling evidence of a strong correlation between vibrational dynamics and ultraslow relaxation, we posed the question if the vibrational dynamics encodes predictive information on DH. Here, we review our results, drawn from molecular-dynamics numerical simulation of polymeric and molecular glass-formers, with a special focus on both the breakdown of the Stokes-Einstein relation between diffusion and viscosity, and the size of the regions with correlated displacements.