  The motion of the structure determining components is highly collective, both
in amorphous solids and in undercooled liquids. This has been deduced from
experimental low temperature data in the tunneling regime as well as from the
vanishing isotope effect in diffusion in glasses and undercooled liquids. In
molecular dynamics simulations of glasses one observes that both low frequency
resonant vibrations and atomic jumps are centered on more than 10 atoms which,
in densely packed materials, form chainlike structures. With increasing
temperature the number of atoms jumping collectively increases. These chains of
collectively jumping atoms are also seen in undercooled liquids. Collectivity
only vanishes at higher temperatures. This collectivity is intimately related
to the dynamic heterogeneity which causes a non-Gaussianity of the atomic
displacements.
