Bifurcation of stretched exponential relaxation in microscopically homogeneous glasses

Measured exponents associated with stretched exponential relaxation (SER) are widely scattered in microscopically heterogeneous glasses, but accurately bifurcate into two “magic” values, 3/5 and 3/7, in a wide variety of microscopically homogeneous glasses. These bifurcated values are derived here from a statistical product model that involves diffusion of excitations to native traps in the presence of short-range forces only, or combined short- and long-range forces, respectively. Bifurcated SER can be used to monitor sample homogeneity. It explains a wide range of experimental data, and even includes multiple aspects of the citation distributions of 20th century science, involving 25 million papers and 600 million citations, and why these changed radically in 1960. It also shows that the distribution of country population sizes has compacted glassy character, and is strongly influenced by migration.

► Stretched exponentials with fractal exponents describe glass dynamics.
► There are two “magic” exponents in microscopically homogeneous glasses.
► The “magic” exponents are derived from nanoscopic heterogeneity with traps.
► Glass dynamics describes many network distributions.
► Examples include citation lengths of 25 million papers with 600 million citations.