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Proc Natl Acad Sci U S A. Feb 1986; 83(4): 848–851.
PMCID: PMC322967

On the relationship among three theories of relaxation in disordered systems

Abstract

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.

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Selected References

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  • Shlesinger MF, Montroll EW. On the Williams-Watts function of dielectric relaxation. Proc Natl Acad Sci U S A. 1984 Feb;81(4):1280–1283. [PMC free article] [PubMed]
  • Huber DL. Statistical model for stretched exponential relaxation in macroscopic systems. Phys Rev B Condens Matter. 1985 May 1;31(9):6070–6071. [PubMed]

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