A structural approach to vibrational properties ranging from crystals to disordered systems.

Many scientists generally attribute the vibrational anomalies of disordered solids to the structural disorder, which, however, is still under intense debate. Here we conduct simulations on two-dimensional packings with a finite temperature, whose structure is tuned from a crystalline configuration to an amorphous one, then the amorphous from very dense state to a relatively loose state. By measuring the vibrational density of states and the reduced density of states, we clearly observe the evolution of the boson peak with the change of the disorder and volume fractions. Meanwhile, to understand the structural origin of this anomaly, we identify the soft regimes of all systems with a novel machine-learning method, where the "softness", a local structural quantity, is defined. Interestingly, we find a strong monotonic relationship between the shape of the boson peak and the softness as well as its spatial heterogeneity, suggesting that the softness of a system may be a new structural approach to the anomalous vibrational properties of amorphous solids.