The origin of the Vogel–Fulcher law near the liquid–glass transition

Taking into account the scattering processes due to random eigenfrequencies and random hopping matrices, we calculate the correlation functions of density fluctuations associated with the particle--hole pairs in the intraband and interband. The correlation functions for the intraband yield sound velocity (proportional to the mean atomic velocity) and diffusion (equal to the relaxation time of atoms multiplied by square of the sound velocity). Those for the interband yield phonons and viscosity (equal to the Maxwell relaxation time multiplied by square of the phonon velocity). The relaxation times and the transport coefficients are governed by the Vogel–Fulcher law through the hopping matrices. Phonons exist in both phases, but sound disappears below the freezing point. The Stokes’ law between diffusion and viscosity holds at higher temperatures, but breaks at lower temperatures.