Atomic tunneling states and low-temperature anomalies of thermal properties in amorphous materials

A general theory of local atomic non-single-well potential in amorphous materials is presented. It is shown that the potentials practically are critical double-well potentials with low spring constants. Two essentially different types of two-level tunneling states in such potentials are found. The spectral density of the states is shown to be smooth under realistic conditions. The respective specific heat logarithmically deviates from the linear temperature dependence and logarithmically or more weakly depends on the measurement time. Both types of the tunneling states can essentially contribute to the specific heat, whereas one of the types is rather more strongly coupled with phonons and determines the phononic thermal conductivity. Some other questions are also discussed.