Glass transition singularities and slow relaxation

Generalized susceptibility for the binary soft-sphere mixtures is computed for the frequency range including both the α and β peaks in a supercooled fluid phase with a super-long-time molecular dynamics simulation. It is shown that the α peak has a non-Debye type frequency dependence and the β peak is essentially of a Debye-type. The slow dynamics is analyzed on the basis of the trapping diffusion model which takes account of two types of diffusive dynamics. With the use of the coherent medium approximation, the frequency dependence of dynamical quantities are shown to agree with the observation. The primary relaxation time is shown to exponentially diverge at a certain temperature below the glass transition point, in line with the Vogel-Fulcher equation. A unified view for the Vogel-Fulcher temperature, the glass transition temperature and the kinetic transition temperature is give on the basis of the trapping diffusion model.