Dynamical universality and vibrational divergence in 2D supercooled liquids, quasicrystals, and crystals.

We investigate the dynamical behavior and vibrational properties of three structurally distinct two-dimensional systems: a supercooled binary liquid, a dodecagonal quasicrystal (DDQC), and a hexagonal crystal. Using molecular dynamics simulations, we find that all three systems exhibit transient caging in the mean-squared displacement and non-Gaussian single-particle displacement statistics. However, the temperature dependence of the dynamics differs markedly among them. In the supercooled liquid, the peak of the non-Gaussian parameter increases upon cooling, reflecting the growth of dynamical heterogeneity. In contrast, in the DDQC, the peak decreases as temperature is lowered, consistent with the progressive suppression of thermally activated, localized rearrangements. For the DDQC, this behavior is confirmed by the cage-relative self part of the van Hove function, which shows a systematic suppression of large single-particle displacements upon cooling. At the same time, the DDQC exhibits a large dynamical susceptibility, indicating that many-body dynamical correlations remain strong despite the reduction of large particle displacements upon cooling. A real-space cluster analysis reveals that mobile particles remain organized into extended, spatially correlated, dynamical clusters, with temperature primarily affecting the cluster-size distribution rather than the intrinsic cluster morphology. The vibrational spectra further differentiate the three systems: the crystal exhibits van Hove singularities, the supercooled liquid shows a boson peak, and the DDQC displays additional low-frequency contributions associated with quasiperiodic order. These results establish the DDQC as an intermediate state, combining glass-like caging dynamics with vibrational signatures strongly influenced by quasiperiodic order.