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Relationship between dynamical heterogeneities and stretched exponential relaxation.

S I Simdyankin1, Normand Mousseau

  • 1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

Dynamical heterogeneities are crucial for stretched exponential relaxation in frustrated systems. Ordered domains with diverging lifetimes lead to stretched exponential relaxation and autocorrelation functions.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Complex systems

Background:

  • Dynamically frustrated systems exhibit complex behaviors not explained by simple exponential decay.
  • Understanding relaxation dynamics is key to characterizing material properties and system evolution.

Purpose of the Study:

  • To identify the essential prerequisites for stretched exponential relaxation.
  • To investigate the role of dynamical heterogeneities in relaxation processes.

Main Methods:

  • Analysis of dynamical heterogeneities in atomic, molecular, and magnetic systems.
  • Characterization of domain lifetimes and their distribution.
  • Rigorous mathematical analysis of renewal processes and autocorrelation functions.

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Main Results:

  • Dynamical heterogeneities, specifically ordered domains with finite but diverging lifetimes, are identified as essential for stretched exponential relaxation.
  • The distribution of time intervals spent in these domains follows a stretched exponential at long times.
  • The autocorrelation function of the associated renewal process also exhibits stretched exponential behavior.

Conclusions:

  • Dynamical heterogeneities are a fundamental requirement for stretched exponential relaxation in dynamically frustrated systems.
  • The observed stretched exponential behavior in relaxation and autocorrelation functions is directly linked to the properties of these ordered domains.