Random Vibrational Networks and Renormalization Group

Abstract

We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several real-space renormalization techniques which can be used to describe this dynamics on general networks, drawing on strong disorder techniques developed for regular lattices. The renormalization group is capable of elucidating the localization properties, and provides, even for specific network instances, a fast approximation technique for determining the spectra which compares well with exact results.

4 pages, 3 figures

References in corpus (5)

• Statistical mechanics of complex networks
• Renormalization group analysis of the small-world network model
• Infinite-randomness quantum Ising critical fixed points
• A single defect approximation for localized states on random lattices
• Correlations between eigenvalues of large random matrices with independent entries

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• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
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• Non-equilibrium dynamics of finite-dimensional disordered systems : RG flow towards an "infinite disorder" fixed point at large times
• Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
• Thermalization of isolated harmonic networks under conservative noise
• Spectral properties of disordered fully-connected graphs
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise
• Reproducing the Kolmogorov spectrum of turbulence with a hierarchical linear cascade model