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Algebraic Decay in Hierarchical Graphs

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Abstract

We study the algebraic decay of the survival probability in open hierarchical graphs. We present a model of a persistent random walk on a hierarchical graph and study the spectral properties of the Frobenius–Perron operator. Using a perturbative scheme, we derive the exponent of the classical algebraic decay in terms of two parameters of the model. One parameter defines the geometrical relation between the length scales on the graph, and the other relates to the probabilities for the random walker to go from one level of the hierarchy to another. The scattering resonances of the corresponding hierarchical quantum graphs are also studied. The width distribution shows the scaling behavior P(Γ)∼1/Γ.

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Authors and Affiliations

  1. Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Felipe Barra & Thomas Gilbert

  2. Dept. Física, Facultad de ciencias Físicas y Matem'aticas universidad de Chile, casilla 487-3, Santiago, Chile

    Felipe Barra

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  1. Felipe Barra
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  2. Thomas Gilbert
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Barra, F., Gilbert, T. Algebraic Decay in Hierarchical Graphs. Journal of Statistical Physics 109, 777–801 (2002). https://doi.org/10.1023/A:1020427018179

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