Numerical Studies of Particle-Like Complex Systems

Many complex physical systems can be modeled as interacting particles and studied via a particle-based model. Such techniques have been widely applied in chemical physics, material science, and biophysics. In this thesis, we study such particle-like complex systems via numerical simulation. We specifically focus on Abrikosov vortices in Type-II superconductors, but extension to other systems is also discussed. We first study Abrikosov vortices coupled to an artificial-spin-ice (ASI) structure. Compared with artificial defects in superconductors in previous studies, ASI provides an in-situ reconfigurable pinning landscape for the Abrikosov vortices, which enables more flexibility to control vortex dynamics. Furthermore, we realize geometrical frustration for the first time in a 2D flux-quanta system. We then study single vortex manipulation via a moving magnetic probe. This provides new insights into vortex operations and can be generalized to other types of particle-based systems. For a systematic study of vortex matter, in particular, vortex matter confined in a mesoscopic container, we adopt a network science approach to generate a compact representation of the full configuration space. We find that for almost all the systems we studied, the ground state is at the “core” of this network, which correlates the energetic property of the system with the topology of its network representation. We further study how system stability depends on container symmetry, container size, and vortex number. We elucidate their effects and explain the emergent “magic number” states, which are extraordinarily stable states at specific vortex numbers.