The Density of Tunneling and Vibrational States of Glasses within the Soft-Potential Model

Numerical calculations of the density of tunneling and vibrational states of glasses within the soft-potential model (an extension of the tunneling model to include soft vibrations) are reported and compared to analytical approximations. Using a specific assumption on the asymmetry of the soft potentials, one is able to describe the anomalous features of the specific heat Cp and the thermal conductivity of glasses over the entire low temperature range, up to and including the peak in Cp/T3 and the second rise of the thermal conductivity above the plateau.