Anomalous frequency dependence of the internal friction of vitreous silica

The internal friction Q(-1) and the sound velocity delta nu/nu of vitreous silica were measured at very low temperatures using mechanical double paddle resonators operated at frequencies ranging from 0.33 to 14 kHz. Below similar to 40 mK the internal friction showed an unexpected temperature and frequency defendence, with absolute values of Q(-1) clearly exceeding those predicted by the standard tunneling model. Even though the most plausible origin of the observed excess internal friction appears to be the mutual interaction between tunneling states, the results are difficult to reconcile quantitatively with present theories taking into account this interaction.