Stability and Magic Number Configurations of Confined Vortex Matter via Network Science

The ground state and dynamics of vortex matter has been widely studied by molecular dynamics (MD) simulation. However, this method only probes a small region of the whole configuration space. For a systematic study of the configuration stability under different conditions, we propose a novel method based on a network science approach. As first shown by Stillinger and Weber, the metastable states (vertices) and the transition states between them (edges) form a complex network with graph theoretical properties that correlate with energetic properties, the stability of metastable n-body configurations and the transitions between them. This network mapping provides a reduced degree complexity description of the n-body system, yet detailed enough to capture novel behavior as function of the confinement geometry and the pinning potential configuration. We implement this method to study the stability of vortex matter as well as identify “magic number” configurations, i.e., ground states with extraordinary high stability at specific vortex number.