Random walk on a fractal: Eigenvalue analysis

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


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.


Spectroscopy Neural Network State Physics Complex System Random Walk 
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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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