Dynamics of quantized vortices under quasi-periodic boundary conditions

Abstract: The Gross-Pitaevskii equation is widely used for vortex dynamics, but finite domains with hard walls or confining potentials distort bulk behavior through vortex-image effects or induced flows. Periodic boundaries reduce wall artifacts yet cannot realize finite net vorticity because of topological obstruction, so bulk simulations with non-zero circulation are typically unavailable. Hence, we impose quasi-periodic boundary conditions that keep the superfluid's density periodic while enforcing phase windings consistent with a net prescribed total vorticity. This setting conserves the net number of vortices and enables long-time tracking of vortex trajectories in settings that finite containers cannot capture. This allows us to study vortex depinning and nucleation leading to the creation of K\'arm\'an vortex streets and the creation of perfectly periodic vortex arrays. The framework also provides a toy model for studying vortex dynamics in the bulk of neutron stars, free of possible limitations induced by confining potentials.