Title: Implications of random matrix models for vibrational modes of glasses

Author (Invited): Lisa Manning, Syracuse University

Abstract:

It is precisely understood how single defects in crystals alter the phonon spectrum. Recently we discovered analogous defects, called soft spots, in disordered solids, but there is no framework for understanding how these defects interact with vibrational modes. A major hurdle to developing such a framework is that the low-frequency modes, which are a mixture of plane-wave like modes and disordered "boson peak" or "anomalous" modes, remain poorly characterized. We have characterized the boson peak eigenvectors by studying the distributions of their component magnitudes. Surprisingly, we find that these "eigenvector distributions" approach a well-defined limiting function, and demonstrate numerically that this function is identical to that for a broad class of random matrix ensembles. Our results suggest that this class of models, which includes the mean field limit of "Euclidean Random Matrices", have eigenvector statistics that belong to a different universality class from the Gaussian Orthogonal Ensemble. Futhermore, we investigate a specific group of "diagonally dominant" random matrices that also reproduce trends in the density of states seen in disordered solids near the jamming transition. These random matrix ensembles provide a tractable starting point for studying the origins of quasi-localized modes associated with soft spots in disordered solids, as well as interactions between modes at low frequencies.