Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 109, Issue 3-4, Pages 777-801Publisher
SPRINGER
DOI: 10.1023/A:1020427018179
Keywords
survival probability; algebraic decay; Pollicott- Ruelle resonances; quantum scattering resonances
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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(Gamma) similar to 1/Gamma.
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