Probing the non-Debye low-frequency excitations in glasses through random pinning

Significance Amorphous solids are continuum media. However, their mechanical and thermodynamical properties, even though universal, dramatically deviate from those in crystalline solids. Their anomalous behavior reflects peculiar and universal deviations from Debye’s law in the low-frequency sector of the density of states D(ω). Theoretical models predict a population of non-Goldstone modes following the universal power law D(ω)∼ω4 that are subdominant and therefore hard to detect. In this work, we introduce a general protocol that can be used in both numerical simulations and experiments, to probe the non-Debye portion of the spectrum. We investigate the properties of the low-frequency spectrum in the density of states D(ω) of a 3D model glass former. To magnify the non-Debye sector of the spectrum, we introduce a random pinning field that freezes a finite particle fraction to break the translational invariance and shifts all of the vibrational frequencies of the extended modes toward higher frequencies. We show that non-Debye soft localized modes progressively emerge as the fraction p of pinned particles increases. Moreover, the low-frequency tail of D(ω) goes to zero as a power law ωδ(p), with 2≤δ(p)≤4 and δ=4 above a threshold fraction pth.

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