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Random walk on a fractal: Eigenvalue analysis

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Zeitschrift für Physik B Condensed Matter

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.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Ruprecht-Karls-Universität, Philosophenweg 19, D-6900, Heidelberg, Federal Republic of Germany

    K. H. Hoffmann & F. Wegner

  2. Fachbereich Physik, Philipps-Universität, Renthof 6, D-3550, Marburg, Federal Republic of Germany

    S. Grossmann

Authors
  1. K. H. Hoffmann
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  2. S. Grossmann
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  3. F. Wegner
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Dedicated to B. Mühlschlegel on the occasion of his 60th birthday

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Hoffmann, K.H., Grossmann, S. & Wegner, F. Random walk on a fractal: Eigenvalue analysis. Z. Physik B - Condensed Matter 60, 401–414 (1985). https://doi.org/10.1007/BF01304462

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  • DOI: https://doi.org/10.1007/BF01304462

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