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Random walk on a fractal: Eigenvalue analysis

  • K. H. Hoffmann
  • S. Grossmann
  • F. Wegner
Article

Abstract

The eigenvalues of the master equation describing the motion on a nested hierarchy ofd-dimensional intervals with selfsimilar scaling of spatial extension as well as of the level dependent transition rates are derived. Based on this spectrum the diffusion behaviour is obtained, which is anomalous, either exponential or obeying a power law with various exponents. Emphasis is put on the insight into the mechanism of the anomalous diffusion, in particular the geometrical structure of the decay rate spectrum.

Keywords

Spectroscopy Neural Network State Physics Complex System Random Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Wegner, F., Grossmann, S.: Z. Phys. B—Condensed Matter59, 197 (1985)Google Scholar
  2. 2.
    Grossmann, S., Wegner, F., Hoffmann, K.H.: J. Phys. (Paris) Lett.46, L-575 (1985)Google Scholar
  3. 3.
    Alexander, S., Bernasconi, J., Schneider, W.R., Orbach, R.J.: Rev. Mod. Phys.53, 175 (1981)Google Scholar
  4. 4.
    Alexander, S., Orbach, R.J.: J. Phys. (Paris) Lett.43, L-625 (1982)Google Scholar
  5. 5.
    Blumen, A., Klafter, J., White, B.S., Zumofen, G.: Phys. Rev. Lett.53, 1301 (1984)Google Scholar
  6. 6.
    Grossmann, S., Thomae, S.: Phys. Lett.97A, 263 (1983)Google Scholar
  7. 7.
    Geisel, T., Thomae, S.: Phys. Rev. Lett.52, 1936 (1984)Google Scholar
  8. 8.
    Geisel, T., Nierwetberg, J., Zacherl, A.: Phys. Rev. Lett.54, 616 (1985)Google Scholar
  9. 9.
    Grossmann, S., Procaccia, I.: Phys. Rev. A29, 1358 (1984)Google Scholar
  10. 10.
    Rammal, R., Toulouse, G.: J. Phys. (Paris) Lett.44, L-13 (1983)Google Scholar
  11. 11.
    O'Shoughnessy, B., Procaccia, I.: Phys. Rev. Lett.54, 455 (1985)Google Scholar
  12. 12.
    Huberman, B.A., Kerszberg, M.: J. Phys. A18, L-331 (1985)Google Scholar
  13. 13.
    Grossmann, S.: Fully developed turbulence as a complex structure in nonlinear dynamics. In: Complex systems-operational approaches. Proceedings of the International Symposium on Synergetics, Schloß Elmau, May 6–11, 1985. Haken, H. (ed.), Berlin, Heidelberg, New York: Springer 1985Google Scholar
  14. 14a.
    Huberman, B.A., Hogg, T.: Phys. Rev. Lett.52, 1048 (1984)Google Scholar
  15. 14b.
    Hogg, T., Huberman, B.A.: Phys. Rev. (to appear)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • K. H. Hoffmann
    • 1
  • S. Grossmann
    • 2
  • F. Wegner
    • 1
  1. 1.Institut für Theoretische PhysikRuprecht-Karls-UniversitätHeidelbergFederal Republic of Germany
  2. 2.Fachbereich PhysikPhilipps-UniversitätMarburgFederal Republic of Germany

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