title: General mapping between random walks and thermal vibrations in elastic networks: fractal networks as a case study.
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.
authors.affiliation: School of Chemistry, Tel-Aviv University, Tel-Aviv 69978, Israel.
authors.forename: Shlomi
authors.initials: S
authors.lastname: Reuveni
authors.forename: Rony
authors.initials: R
authors.lastname: Granek
authors.forename: Joseph
authors.initials: J
authors.lastname: Klafter
mesh_terms: D004548:Elasticity; D017709:Fractals; D008962:Models, Theoretical; D013269:Stochastic Processes; D013696:Temperature; D014732:Vibration