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Spatial structure of quasi-localized vibrations in nearly jammed amorphous solids
The low-temperature properties of amorphous solids are widely believed to be
controlled by low-frequency quasi-localized modes. What governs their spatial
structure and density is however debated. We study these questions numerically
in very large systems as the jamming transition is approached and the pressure
p vanishes. We find that these modes consist of an unstable core in which
particles undergo the buckling motions and decrease the energy, and a stable
far-field component which increases the energy and prevents the buckling of the
core. The size of the core diverges as and its characteristic volume
as These features are precisely those of the anomalous modes known
to cause the Boson peak in the vibrational spectrum of weakly-coordinated
materials. From this correspondence we deduce that the density of
quasi-localized modes must go as ,
in agreement with previous observations. Our analysis thus unravels the nature
of quasi-localized modes in a class of amorphous materials.Comment: 5 pages, 4 figure
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