Why the fast relaxation in the picosecond to nanosecond time range can sense the glass transition

The fast relaxation measured by quasielastic neutron and light scattering on the picosecond to nanosecond time scales when expressed as mean square displacement as a function of temperature shows a change in slope at or near the conventional glass transition temperature in a manner like those of the enthalpy and volume. This behaviour of the fast relaxation is puzzling because the glass transition originates from the structure of the liquid falling out of equilibrium at temperatures where the alpha-relaxation time becomes long, for example 10(3) s. In this work, we consider a model proposed for the fast relaxation that is based on an extension of the coupling model to incorporate the dynamics of cage decay. Several properties of the fast relaxation are deduced from the model and shown to be consistent with the experimental data, including the appearance of a break at the glass transition temperature.