The role of excitations in supercooled liquids: Density, geometry, and relaxation dynamics.

Low-energy excitations play a key role in all condensed-matter systems, yet there is limited understanding of their nature in glasses, where they correspond to local rearrangements of groups of particles. Here, we introduce an algorithm to systematically uncover these excitations up to the activation energy scale relevant to structural relaxation. We use it in a model system to measure the density of states on a scale never achieved before, confirming that this quantity shifts to higher energy under cooling, precisely as the activation energy does. Second, we show that the excitations' energetic and spatial features allow one to predict with great accuracy the dynamic propensity, i.e., the location of future relaxation dynamics. Finally, we find that excitations have a primary field whose properties, including the displacement of the most mobile particle, scale as a power-law of their activation energy and are independent of temperature. Additionally, they exhibit an outer deformation field that depends on the material's stability and, therefore, on temperature. We build a scaling description of these findings. Overall, our analysis supports that excitations play a crucial role in regulating relaxation dynamics near the glass transition, effectively suppressing the transition to dynamical arrest predicted by mean-field theories while also being strongly influenced by it.