Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation
<|reference_start|>Numerical study of the Gross-Pitaevskii equation on a two-dimensional ring and vortex nucleation: We consider the Gross-Pitaevskii equation with a confining ring potential with a Gaussian profile. By introducing a rotating sinusoidal perturbation, we numerically highlight the nucleation of quantum vortices in a particular regime throughout the dynamics. Numerical computations are made via a Strang splitting time integration and a two-point flux approximation Finite Volume scheme based on a particular admissible triangulation. We also develop numerical algorithms for vortex tracking adapted to our finite volume framework.<|reference_end|>
@article{chauleur2024numerical,
    title={Numerical study of the Gross-Pitaevskii equation on a two-dimensional
  ring and vortex nucleation},
    author={Quentin Chauleur (PhLAM, Paradyse), Radu Chicireanu (PhLAM), Guillaume
  Dujardin (Paradyse, LPP), Jean-Claude Garreau (PhLAM), Adam Ranc{c}on
  (PhLAM)},
    journal={arXiv preprint arXiv:2404.10360},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10360},
    primaryClass={math.NA cond-mat.quant-gas cs.NA physics.comp-ph}
}