Journal of Statistical Physics

, Volume 109, Issue 3–4, pp 777–801 | Cite as

Algebraic Decay in Hierarchical Graphs

  • Felipe Barra
  • Thomas Gilbert

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.

Survival probability algebraic decay Pollicott–Ruelle resonances quantum scattering resonances 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Felipe Barra
    • 1
    • 2
  • Thomas Gilbert
    • 1
  1. 1.Department of Chemical PhysicsThe Weizmann Institute of ScienceRehovotIsrael
  2. 2.Dept. FísicaFacultad de ciencias Físicas y Matem'aticas universidad de ChileSantiagoChile

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