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

摘要

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(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* 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*) in the low-frequency power law D(omega) similar to omega(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 xi(3) proportional to p. Finally, we provide an estimate of xi as a function of T*, finding a mild power law divergence, xi similar to(T* -T-d)(-alpha/3), with T-d the dynamical crossover temperature and a falling in the range alpha is an element of [0.8,1.0].