Thermal conductivity in amorphous solids at temperatures below 1 K

Recently derived distribution functions for the intrinsic two-level systems (ITLS’s) of glasses are used to calculate the temperature power laws for the thermal conductivity (κ) and specific heat ($C_V$). The previously noted ‘‘apparent’’ discrepancy between the two power laws is shown to be the result of an insufficiently accurate approximation used in the averaging of κ over the TLS distribution. Good agreement with the κ and $C_V$ data for vitreous silica is obtained when distribution-function parameters appropriate for ITLS’s are employed.