Random Vibrational Networks and Renormalization Group

Details Random Vibrational Networks and Renormalization Group Random Vibrational Networks and Renormalization Group

2002-12-12

arxiv.org/abs/cond-mat/0212303v1

Phys. Rev. Lett. 90, 148702 (2003).

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.90.148702

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.

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