0030-400X/05/9805- $26.00 © 2005 Pleiades Publishing, Inc. 0740 Optics and Spectroscopy, Vol. 98, No. 5, 2005, pp. 740–746. Translated from Optika i Spektroskopiya, Vol. 98, No. 5, 2005, pp. 806–813. Original Russian Text Copyright © 2005 by Vaœner, Naumov, Bauer, Kador, Barkai. 1. INTRODUCTION Solid-state disordered media, to which the widest variety of materials and objects with local inhomogene- ities and disorder in the internal structure can be assigned, are widespread in nature and find a broad spectrum of applications in practice. These are various crystals with a great number of internal defects and ran- dom impurities, a wide class of glasses and ceramics, various polymers, amorphous metals and semiconduc- tors, many nanoobjects and clusters, the majority of biological media in a frozen state, and so on. However, the studies of the physical properties of disordered solid-state substances that have been carried out in recent years are drastically outnumbered by the studies of crystals. This fact can be explained by the relative simplicity of the internal structure of highly ordered materials having a high degree of symmetry. The appli- cation of standard physical approaches and methods, developed over many years of studying the properties of perfect crystals, to investigations of disordered mat- ter in most cases turns out to be ineffective or impossi- ble. The necessity of developing our knowledge of the nature and properties of solids and the increasing demands of practice make investigations of the proper- ties of disordered solids more and more urgent. Study of the dynamics of disordered solid-state mat- ter in the region of low and intermediate temperatures is one of the important trends in modern solid-state physics. 1 Temperatures below a few kelvins are gener- ally classified as low temperatures, and temperatures from a few to several tens of kelvins, as intermediate temperatures. The first experimental studies of the low- temperature dynamic properties of glasses, started in the 1970s, demonstrated that these properties differ sharply from the corresponding properties of crystals. It also turned out that the dynamic properties of these sub- stances are universal in nature and are virtually inde- pendent of their concrete composition and structure. These observations clearly indicated that the observed anomalous dynamic properties of glasses are caused not by a specific structure of a sample under study but by the very existence of internal disorder in the spatial arrangement of atoms and molecules in such materials. Thus, explanation of the anomalous properties of glasses at low and intermediate temperatures required an understanding of the dynamic behavior of atoms or molecules in a solid in the case where ordering in their location is absent. From a purely mathematical point of view, the problem seemed to be practically unsolvable. The situation changed sharply when Anderson and coauthors [1] and, independently, Philips [2] advanced a brilliant idea about the existence in amorphous media of elementary low-energy excitations—tunneling two- level systems (TLSs)—that are specific to these media. 1 In this paper, for the sake of simplicity, all kinds of disordered solids will be called glasses, as is accepted in the literature. Statistical Analysis of Spectra of Single Impurity Molecules and Dynamics of Disordered Solids: I. Distributions of Linewidths, Moments, and Cumulants Yu. G. Vaœner*, A. V. Naumov*, M. Bauer**, L. Kador**, and E. Barkai*** * Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow oblast, 142190 Russia ** Institute of Physics and Bayreuther Institut für Makromolekülforschung, University of Bayreuth, D-95440 Bayreuth, Germany *** University of Notre Dame, Notre Dame, IN 46556, USA e-mail: vainer@isan.troitsk.ru Received November 1, 2004 Abstract—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 per- formed in the range 2–7 K. The use of SMS allowed us to avoid the information losses connected with the aver- aging over an ensemble of impurity molecules that is inherent in conventional spectral methods. For the exam- ple 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. © 2005 Pleiades Publishing, Inc.