Dynamic structure factor of fractals

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Abstract

The dynamic structure factor S(q,ω) of the vibrational modes of a deterministic fractal is analyzed as a function of both frequency (ω) and momentum (q) transfer. It is found that S(q,ω) is peaked at qmaxω2(2+θ), where θ is the anomalous diffusion exponent, and is a scaling function of q(2+θ)2/ω. The results are obtained by a novel recursion method for the calculation of the vibration Green's function of a deterministic fractal. They confirm predictions based upon the fracton scaling model.

References (13)

  • S. Alexander et al.

    J. Phys. (Paris)

    (1982)
  • S. Alexander

    Ann. Israel Phys. Soc.

    (1983)
    R. Orbach

    Science

    (1986)
    O. Entin-Wohlman
  • K. Yakubo et al.

    Phys. Rev. B

    (1987)
  • E. Courtens et al.

    Phys. Rev. Lett.

    (1987)
    R. Vacher et al.

    Phys. Rev. B

    (1988)
    E. Courtens et al.

    Europhys. Lett.

    (1988)
    Y. Tsujimi et al.

    Phys. Rev. Lett.

    (1988)
  • Y.J. Uemura et al.

    Phys. Rev. B

    (1987)
  • Y. Gefen et al.

    Phys. Rev. Lett.

    (1983)
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