Relation between Heterogeneous Frozen Regions in Supercooled Liquids and Non-Debye Spectrum in the Corresponding Glasses.

Recent numerical studies on glassy systems provide evidence for a population of non-Goldstone modes (NGMs) in the low-frequency spectrum of the vibrational density of states D(ω). 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^{} modifies the GM/NGM ratio in D(ω). In particular, the phonon attenuation is reflected in a parental temperature dependency of the exponent s(T^{}) in the low-frequency power law D(ω)∼ω^{s(T^{})}, with 2≤s(T^{})≤4. Second, by comparing s(T^{}) with s(p), i.e., the same quantity obtained by pinning a p particle fraction, we suggest that s(T^{}) reflects the presence of dynamical heterogeneous regions of size ξ^{3}∝p. Finally, we provide an estimate of ξ as a function of T^{}, finding a mild power law divergence, ξ∼(T^{}-T_{d})^{-α/3}, with T_{d} the dynamical crossover temperature and α falling in the range α∈[0.8,1.0].