A quantum field theory of diffusion near the liquid-glass transition

Randomly distributed atoms are considered in the harmonic potentials with random eigenfrequencies. The hopping of atoms makes energy dispersion curves of an atom. The correlation functions of density fluctuations in the intraband transition yield the freezing point, where the hopping is prohibited. The entropy due to the density fluctuations in the intraband transition yields the hopping matrix which shows the Vogel-Fulcher law. The diffusion is determined by the randomness of the eigenfrequencies and the hopping matrices. The diffusion coefficient is proportional to the first or third power of the configurationally averaged hopping matrix at high or low temperatures, respectively, and obeys the Vogel-Fulcher law. The randomness of eigenfrequencies and hopping matrices also yields the relaxation time of atoms, which obscures the liquid-glass transition.