Acoustic Properties of Amorphous Solids at Very Low Temperatures: The Quest for Interacting Tunneling States

We discuss the strain dependence of the acoustic properties of amorphous metals in both normal and superconducting states, in the temperature range 0.1 mK $ \le T \le 1 $K. A crossover is found when the strain energy is of the order of the effective interaction energy between tunneling systems at the corresponding temperature. Our results provide clear evidence for the interaction between tunneling systems, whose energy is in quantitative agreement with theoretical expectations, and reveal that without the knowledge of the corresponding strain dependences, the measured temperature dependences below $\sim 50 $mK of the acoustic properties of disordered solids are rather meaningless.