Vibrational spectrum derived from local mechanical response in disordered solids

Soft Matter
Masanari ShimadaAtsushi Ikeda

Abstract

The low-frequency vibrations of glasses are markedly different from those of crystals. These vibrations have recently been categorized into two types: spatially extended vibrations, whose vibrational density of states (vDOS) follows a non-Debye quadratic law, and quasilocalized vibrations (QLVs), whose vDOS follows a quartic law. The former are explained by elasticity theory with quenched disorder and microscopic replica theory as being a consequence of elastic instability, but the origin of the latter is still debated. Here, we show that the latter can also be directly derived from elasticity theory with quenched disorder. We find another elastic instability that the theory encompasses but that has been overlooked so far, namely, the instability of the system against a local dipolar force. This instability gives rise to an additional contribution to the vDOS, and the spatial structure and energetics of the mode originating from this instability are consistent with those of the QLVs. Finally, we construct a model in which the additional contribution to the vDOS follows a quartic law.

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Citations

Nov 10, 2020·Soft Matter·Masanari ShimadaAtsushi Ikeda
Oct 24, 2020·The Journal of Chemical Physics·Hideyuki MizunoStefano Mossa
Feb 26, 2020·Proceedings of the National Academy of Sciences of the United States of America·Corrado RainoneEdan Lerner
May 1, 2021·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Naoya TomoshigeNobuyuki Matubayasi

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