Renormalization Group in Dynamical Processes on Hierarchical Networks Open Access

Li, Shanshan (2017)

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Hierarchical structures have been found in actual complex systems. Certain hierarchical networks, with a self-similar structure, exhibit novel properties in a broader spectrum of dynamics such as synchronization, quantum walks and the epidemic process, which we explore in this thesis by applying analytical and numerical methods. We study the structural and spectral properties of large scale networks, as well as various phenomena on them with the Renormalization Group (RG) approach. In particular, by applying RG, we explore the Laplacian spectrum, whichis related to asymptotic structural features of networks, ranging from the number of spanning trees to synchronizability. The spectralanalysis also reveals a deep connection between dynamics and the underlying structure in processes that include quantum walks and the unusual Griffiths phase on hierarchical networks considered in this thesis. This thesis highlights effects of spectral properties on dynamical processes on networks, and indicates the applicability of RG to various contexts.

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