Random Vibrational Networks and Renormalization Group

TL;DR

This paper explores vibrational dynamics on random networks with random masses and springs, using renormalization group techniques to analyze localization and spectra efficiently.

Contribution

It introduces real-space renormalization methods for vibrational networks, extending strong disorder techniques to complex random network structures.

Findings

Renormalization group effectively characterizes localization properties.

The methods provide fast approximations of spectra matching exact results.

Vibrational eigenstates differ significantly from Laplacian cases on these networks.

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.