A quantum field theory of thermal conductivity near the liquid-glass transition

Taking into account the random scatterings due to random eigenfrequencies and random hopping matrices, we obtain the correlation functions for phonon and sound density fluctuations, which yield three and one entropy fluctuation modes at high frequencies, and three and one thermal conductivity at low frequencies, respectively. The relaxation times of the entropy fluctuation modes due to phonons and sound are essentially equal to those of phonons and sound modified by the contributions of the corresponding inverse frequencies which appear in the self-energy part of phonons and sound, respectively. The velocity of phonons almost does not depend on temperatures, but that of sound obeys the Vogel–Fulcher law. The Vogel–Fulcher law on the transport coefficients and the relaxation times due to phonon density fluctuations is in the same form as phonons, but in the different form between the sound and sound density fluctuations. The specific heat due to phonons and sound is also calculated.