Network Science Approach to Confined Vortex Matter

Previous studies of confined vortex matter typically focus on ground state or a single dynamical process. Although metastable states are less studied, they are important to the dynamics and stability of the system. In order to perform a systematic study of these properties, we propose a 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, serving as a concise representation of the potential energy landscape. By applying this method to confined vortex matter, we study the network properties as a function of vortex number and confinement geometry. We show that the ground state is always at the “core” of this network, which justifies the use of simulated annealing via molecular dynamics simulations, in finding the ground state. Furthermore, from transition properties restricted by network topology, we study the stability of vortex matter as well as identify “magic number” configurations, i.e., ground states with high stability at specific vortex numbers.