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 $p^{-1/4}$ and its characteristic volume as $p^{-1/2}$ 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 $g_{\mathrm{loc}}(\omega) \sim \omega^4/p^2$ , 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

Arrhenius temperature dependence of the crystallization time of deeply supercooled liquids

Usually, supercooled liquids and glasses are thermodynamically unstable against crystallization. Classical nucleation theory (CNT) has been used to describe the crystallization dynamics of supercooled liquids. However, recent studies on overcompressed hard spheres show that their crystallization dynamics are intermittent and mediated by avalanche-like rearrangements of particles, which largely differ from the CNT. These observations suggest that the crystallization times of deeply supercooled liquids or glasses cannot be described by the CNT, but this point has not yet been studied in detail. In this paper, we use molecular dynamics simulations to study the crystallization dynamics of soft spheres just after an instantaneous quench. We show that although the equilibrium relaxation time increases in a super-Arrhenius manner with decreasing temperature, the crystallization time shows an Arrhenius temperature dependence at very low temperatures. This is contrary to the conventional formula based on the CNT. Furthermore, the estimated energy barrier for the crystallization is surprisingly small compared to that for the equilibrium dynamics. By comparing the crystallization and aging dynamics quantitatively, we show that a coupling between aging and crystallization is the key for understanding the rapid crystallization of deeply supercooled liquids or glasses.Comment: 8 pages, 4 figure