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Geometric origin of excess low-frequency vibrational modes in amorphous solids

Matthieu Wyart·Sidney R. Nagel·T. A. Witten
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Abstract

Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the density of states of a recently simulated system, comprised of weakly compressed spheres at zero temperature. We account for the observed a) constancy of the density of modes with frequency, b) appearance of a low-frequency cutoff, and c) power-law increase of this cutoff with compression. We predict a length scale below which vibrations are very different from those of a continuous elastic body.

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Matthieu Wyart, Sidney R. Nagel, T. A. Witten. 2005-09-21. Geometric origin of excess low-frequency vibrational modes in amorphous solids. https://doi.org/10.1209/epl%2Fi2005-10245-5

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