Bifurcation of Stretched Exponential Relaxation in Microscopically Homogeneous Glasses

TL;DR

This paper reveals that the exponents of Stretched Exponential Relaxation in homogeneous glasses bifurcate into two universal values, 3/5 and 3/7, explained by a statistical model involving diffusion and traps.

Contribution

It introduces a model explaining the bifurcation of SER exponents in homogeneous glasses and links this to sample homogeneity and broader citation and population distributions.

Findings

SER exponents bifurcate into 3/5 and 3/7 in homogeneous glasses.

The bifurcation can be used to assess sample homogeneity.

The model explains citation distribution changes and population dynamics.

Abstract

Measured exponents associated with Stretched Exponential Relaxation (SER) are widely scattered in microscopically inhomogeneous 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.