Statistical analysis of spectra of single impurity molecules and dynamics of disordered solids: I. Distributions of linewidths, moments, and cumulants

A review of recent results of studying the low-temperature dynamics of a disordered solid-state medium that were obtained by the method of single molecule spectroscopy (SMS) is presented. The studies were carried out with the use of the new approach of the statistical analysis of a large number of spectra of single molecules embedded into a medium under study as a microscopic spectral probe. The measurements were performed in the range 2–7 K. The use of SMS allowed us to avoid the information losses connected with the averaging over an ensemble of impurity molecules that is inherent in conventional spectral methods. For the example of the system studied (amorphous polyisobutylene doped with molecules of tetra-tert-butylterrylene), it was shown experimentally that, at low temperatures, the spectra of single impurity molecules in disordered media obey the Levy statistics. New microscopic information on the interaction of two-level systems and quasi-local low-frequency vibrational modes of the matrix with impurity molecules in a disordered medium was obtained.