General mapping between random walks and thermal vibrations in elastic networks: Fractal networks as a case study

Shlomi Reuveni, Rony Granek, Joseph Klafter

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

We present an approach to mapping between random walks and vibrational dynamics on general networks. Random walk occupation probabilities, first passage time distributions and passage probabilities between nodes are expressed in terms of thermal vibrational correlation functions. Recurrence is demonstrated equivalent to the Landau-Peierls instability. Fractal networks are analyzed as a case study. In particular, we show that the spectral dimension governs whether or not the first passage time distribution is well represented by its mean. We discuss relevance to universal features arising in protein vibrational dynamics.

Original languageEnglish
Article number041132
JournalPhysical Review E
Volume82
Issue number4
DOIs
StatePublished - 29 Oct 2010

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