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Long range diffusion in ultrametric spaces

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Zeitschrift für Physik B Condensed Matter

Abstract

A model for diffusion in spaces with ultrametric topology is introduced. The parameters of the model are two sets of numbers: the branching numberm l+1 /m l describing the hierarchical structure of the metric and the transition ratesr l between different levels of the hierarchy. This model is expected to be relevant to the spin glas problem. The exact solution of the dynamical problem can be given in the general case. In the special casem l =m l andr l ∼R l anomalous long time behaviour of the autocorrelation function is found which decays with a power law multiplied by a periodically varying amplitude.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-5000, Köln 41, Federal Republic of Germany

    M. Schreckenberg

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  1. M. Schreckenberg
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Additional information

Dedicated to B. Mühlschlegel on the occasion of his 60th birthday

This work has been supported by the Sonderforschungsbereich 125, Aachen-Jülich-Köln

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Schreckenberg, M. Long range diffusion in ultrametric spaces. Z. Physik B - Condensed Matter 60, 483–488 (1985). https://doi.org/10.1007/BF01304471

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  • DOI: https://doi.org/10.1007/BF01304471

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