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Lecture notes in physics

Vortex Dynamics

Carlo F. Barenghi, Thomas Bland, Nick G. Parker

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1007/978-3-032-20171-3_9

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A vortex molecule is a topological excitation in two coherently coupled superfluids consisting of a vortex in each superfluid connected by a domain wall of the relative phase, also known as a Josephson vortex. We investigate the dynamics of this excitation in a quasi-two-dimensional geometry with slab or channel boundary conditions using an extended point-vortex framework complemented by Gross-Pitaevskii simulations. Apart from translational motion along the channel, the vortex molecule is found to exhibit intriguing internal dynamics including rotation and rotational-pendulum-like dynamics. Trajectories leading to a boundary-induced breakup of the vortex molecule are also described qualitatively by the simplified model. We classify the stable and unstable fixed points as well as separatrices that characterize the vortex molecule dynamics.
We study the vortex dynamics in the hydrodynamic representation of quantum mechanics for two particles, in which a pointlike vortex comes from a nonintegrable phase of a wavefunction. In particular, we introduce an ansatz for an entangled state of the two particles and discuss how entanglement affects the dynamics of vortex-vortex interaction. For this purpose, we employ the time-dependent quantum variational principle combined with the Rayleigh-Ritz method and elucidate the effects of entanglement on the approximate vortex dynamics.
Abstract We investigate the collisional dynamics of two vortex dipoles in a uniform two-dimensional Bose–Einstein condensate. It is found that the dynamics are deeply related to the moving directions and sizes of the initial vortex dipoles. For the oblique collisions of two vortex dipoles with the same size, we find that the vortices in the two initial vortex dipoles recombine into two new vortex dipoles which scatter in the opposite directions. For the catching-up processes of two vortex dipoles with different size, we find that the faster vortex dipole speeds up and passes through the slower vortex dipole. If the size of the vortex dipoles are small, we also observe vortex annihilation and vortex resurrection. The corresponding parameter ranges of different collisional dynamics are discussed.