Acoustic properties of quantum glasses at low temperatures

The low-temperature thermal and acoustic properties of amorphous solids can be explained in terms of the phenomenological tunneling model (TM).  This  postulates the existence of low energy excitations which can be treated in the two-level approximation. Using the TM we were able to successfully describe the acoustic response of metallic and dielectric glasses.

Image-Source: J. Stockburger et al., Phys. Rev. B 51, 2835 (1995)

Figure:
Temperature dependence of the sound velocity of an insulating glass for different strain levels.

See some key publications:

Nonlinear acoustic properties of glasses in the tunneling model
J. Stockburger, M. Grifoni and M. Sassetti
Phys. Rev. B 51, 2835 (1995)

Nonlinear acoustic response of amorphous metals in the Tunneling Model,
J. Stockburger, M. Grifoni, M. Sassetti, and U. Weiss
Z. Phys. B 94, 447 (1994)