Inferring the particle-wise dynamics of amorphous solids from the local structure at the jamming point

Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their static critical properties with a unified approach. However, the dynamics occurring in the vicinity of the jamming point has received little attention and the problem of finding a connection with the local structure of the configuration remains unexplored. Here we address this issue by constructing physically well defined structural variables using the information contained in the network of contacts of jammed configurations, and then showing that such variables yield a resilient statistical description of the particle-wise dynamics near this critical point. Our results are based on extensive numerical simulations of systems of spherical particles that allow us to statistically characterize the trajectories of individual particles in terms of their first two moments. We first demonstrate that, besides displaying a broad distribution of mobilities, particles may also have preferential directions of motion. Next, we associate each of these features with a structural variable computed uniquely in terms of the contact vectors at jamming, obtaining considerably high statistical correlations. The robustness of our approach is confirmed by testing two types of dynamical protocols, namely molecular dynamics and Monte Carlo, with different types of interaction. We also provide evidence that the dynamical regime we study here is dominated by anharmonic effects and therefore it cannot be described properly in terms of vibrational modes. Finally, we show that correlations decay slowly and in an interaction-independent fashion, suggesting a universal rate of information loss.