On the relationship among three theories of relaxation in disordered systems

Empirical evidence has accumulated showing the wide occurrence of a stretched-exponential relaxation decay law for many diverse condensed-matter systems. Several theories based on different physical mechanisms have been successful in deriving the stretched-exponential decay law in a natural way. Three of these theories, the direct-transfer model, the hierarchically constrained dynamics model, and the defect-diffusion model are shown here to have an underlying common mathematical structure.