Random walk on a fractal: Eigenvalue analysis |
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Authors: | K H Hoffmann S Grossmann F Wegner |
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Institution: | (1) Institut für Theoretische Physik, Ruprecht-Karls-Universität, Philosophenweg 19, D-6900 Heidelberg, Federal Republic of Germany;(2) Fachbereich Physik, Philipps-Universität, Renthof 6, D-3550 Marburg, Federal Republic of Germany |
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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.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday |
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