Statistics and properties of low-frequency vibrational modes in structural glasses

Abstract

Low-frequency vibrational modes play a central role in determining various basic properties of glasses, yet their statistical and mechanical properties are not fully understood. Using extensive numerical simulations of several model glasses in three dimensions, we show that in systems of linear size $L$ sufficiently smaller than a crossover size $L_D$, the low-frequency tail of the density of states follows $D(\omega )\sim {\omega }^4$ up to the vicinity of the lowest Goldstone mode frequency. We find that the sample-to-sample statistics of the minimal vibrational frequency in systems of size $L<L_D$ is Weibullian, with scaling exponents in excellent agreement with the ${\omega }^4$ law. We further show that the lowest frequency modes are spatially quasi-localized, and that their localization and associated quartic anharmonicity are largely frequency-independent. The effect of preparation protocols on the low-frequency modes is elucidated and a number of glassy lengthscales are briefly discussed.

Missing detail added to the supplemental material, see also: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.099901

References in corpus (11)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Fractal free energy landscapes in structural glasses
• Irreversible reorganization in a supercooled liquid originates from localised soft modes
• Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
• Suppression of tunneling two-level systems in ultrastable glasses of indomethacin
• Energy transport in jammed sphere packings
• Universal non-Debye scaling in the density of states of amorphous solids
• Nonlinear plastic modes in disordered solids
• Soft Modes, Localization and Two-Level Systems in Spin Glasses
• The micromechanics of nonlinear plastic modes
• On the spatial distribution of thermal energy in equilibrium

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