Scaling Theories for Anomalous Dynamics on Fractals: Fractons

  • Amnon Aharony
  • Ora Entin-Wohlman
  • R. Orbach
Part of the NATO ASI Series book series (volume 167)


Many systems in nature exhibit different geometrical structures at different length scales. Although they are homogeneous (on the average) for large length scales, they exhibit self-similarity on short length scales. In the latter case such systems may be modeled by fractal structures.1 On a fractal structure, all the physical properties behave as powers of the relevant length scale. This behavior crosses over to a homogeneous one, similar to that of usual bulk matter, at a crossover length, called ξ. Assuming that ξ is the only relevant length scale in the problem, the dependence on any other length L should arise via the ratio L/ξ. A typical intrinsic quantity χ will have the “fractal” behavior χ~Lx for L«ξ, and will crossover to a size independent behavior, χ~ξx, for L>>ξ.


Fractal Structure Fractal Dimensionality Crossover Frequency Excitational Mode Large Length Scale 
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Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Amnon Aharony
    • 1
  • Ora Entin-Wohlman
    • 2
  • R. Orbach
    • 3
  1. 1.School of Physics and Astronomy Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Laboratoire de Physique des SolidesUniversite Paris-SudOrsayFrance
  3. 3.Department of PhysicsUniversity of CaliforniaLos AngelesUSA

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