Frequency Spectrum and Low-Temperature Specific Heat of Noncrystalline Solids

It is shown that an extra phonon density of states associated with the roton-like part of the dispersion of phonon excitations, which is likely to exist in almost all types of noncrystalline solids, gives rise to an excess low-temperature specific heat. This could account for the anomaly in the low-temperature thermal properties observed in a large number of noncrystalline solids and glassy polymers. It is shown that under certain conditions the excess low-temperature specific heat is nearly proportional to absolute temperature.