Experiments and theory of the nonexponential relaxation in liquids, glasses, polymers and crystals

More than 130 years ago it was first recognized that the observed response from many diverse substances may exhibit two distinct types of nonexponential relaxation. Although the Kohlrausch-Williams-Watts (KWW) stretched exponential and Curie-von Schweidler (CvS) power law have since been used to characterize the observed response from thousands of measurements, there is still no commonly accepted explanation for these empirical formulas. Only in the past few years have there been experimental techniques developed to answer the most basic question about the observed response: is it homogeneous where all regions of the sample exhibit intrinsic nonexponential behavior, or is it a result of a heterogeneous distribution of relaxation times? One technique, nonresonant spectral hole burning (NSHB), uses a large amplitude, low-frequency electric- or magnetic-field to selectively investigate the constituents in the net spectrum of response. An important advantage of NSHB is that the responding degrees of freedom are used directly as their own local probe. For all systems examined so far, including amorphous and crystalline materials, the nonexponential relaxation is found to result from a distribution of relaxation times. This raises the theoretical questions: why are there two types of nonexponential behavior, and why are they so "universal"? A possible answer comes from a mesoscopic model for nonexponential relaxation that provides a common physical basis for both universalities.