Dynamics on ultrametric spaces

Andrew T. Ogielski, D. L. Stein

Research output: Contribution to journalArticle


We present an exact solution to the problem of a random walk on an ultrametric space with arbitrary transition probabilities. The solution provides a description of fluctuation dynamics of systems with many degenerate states separated by a hierarchy of energy barriers. Dynamical behavior is found to depend on the scaling of barriers with ultrametric distance. We find a range of interesting behavior, from temperature-dependent power-law decay to the Kohlrausch law.

Original languageEnglish (US)
Pages (from-to)1634-1637
Number of pages4
JournalPhysical Review Letters
Issue number15
StatePublished - Jan 1 1985
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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