Relation between heterogeneous frozen regions in supercooled liquids and non-Debye spectrum in the corresponding glasses

Abstract

Recent numerical studies on glassy systems provide evidences for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states $D(\omega )$. Similarly to Goldstone modes (GMs), i. e., phonons in solids, NGMs are soft low-energy excitations. However, differently from GMs, NGMs are localized excitations. Here we first show that the parental temperature $T^{\ast }$ modifies the GM/NGM ratio in $D(\omega )$. In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent $s(T^{\ast })$ in the low-frequency power law $D(\omega )\sim {\omega }^{s(T^{\ast })}$, with $2\le s(T^{\ast })\le 4$. Secondly, by comparing $s(T^{\ast })$ with $s(p)$, i. e., the same quantity obtained by pinning \mttp{a} $p$ particle fraction, we suggest that $s(T^{\ast })$ reflects the presence of dynamical heterogeneous regions of size ${\xi }^3\propto p$. Finally, we provide an estimate of $\xi$ as a function of $T^{\ast }$, finding a mild power law divergence, $\xi \sim (T^{\ast }-T_d{)}^{-\alpha /3}$, with $T_d$ the dynamical crossover temperature and $\alpha$ falling in the range $\alpha \in [0.8,1.0]$.

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• Finite-size effects in the nonphononic density of states in computer glasses
• The nature of non-phononic excitations in disordered systems
• Universal non-Debye low-frequency vibrations in sheared amorphous solids
• Density of States below the First Sound Mode in 3D Glasses
• Relationship between two-level systems and quasi-localized normal modes in glasses
• Random quench predicts universal properties of amorphous solids
• Further testing the validity of generalized heterogeneous-elasticity theory for low-frequency excitations in structural glasses
• Low-frequency excitations and their localization properties in glasses