THE LOW-ENERGY COLLECTIVE EXCITATIONS IN DIELECTRIC GLASSES - THE ATTENUATION OF SOUND-WAVES AT ULTRA-LOW TEMPERATURES

The up-down interaction between two-level systems in dielectric glasses leads to arising of space-delocalized low-energy excitations subsystem. In the case of ultra low temperatures when the phonons are significantly frozen out the relaxation processes will be defined by the excitations of the subsystem. The low-frequency sound attenuation is studied. It is shown that the attenuation coefficient demonstrates crossover from the known phonon-induced behaviour alpha approximately T3 to alpha approximately T at sufficiently low temperature. This behaviour was recently discovered in amorphous SiO2 [1].