Understanding the statistical mechanics of low-energy excitations in structural glasses has been the focus of extensive research efforts in the past decades due to their key roles in determining the low-temperature mechanical and transport properties of these intrinsically nonequilibrium materials. While it is established that glasses feature low-energy nonphononic excitations that follow a non-Debye vibrational density of states, we currently lack a well-founded theory of these fundamental objects and their vibrational spectra. A recent theory—that builds on the so-called heterogeneous-elasticity theory (HET) and its extensions—provides explicit predictions for the scaling of the low-frequency tail of the nonphononic spectrum of glasses, the localization properties of the vibrational modes that populate this tail, and its connections to glass formation history and to the form of the distribution of weak microscopic (interatomic) stresses. Here, we employ computer models of structural glasses to quantitatively test these predictions. Our findings do not support the HET's predictions regarding the nature and statistics of low-energy excitations in glasses, highlighting the need for additional theoretical developments.

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• Stress
• Vibrational states
• Glasses