English

Hamiltonian derivation of the point vortex model from the two-dimensional nonlinear Schr\"odinger equation

Fluid Dynamics 2023-03-06 v3 Quantum Gases Mathematical Physics math.MP Pattern Formation and Solitons Optics

Abstract

We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schr{\"o}dinger equation, from the Hamiltonian perspective, in the limit of well-separated, subsonic vortices on the background of a spatially-infinite strong condensate. As a corollary, we calculate to high accuracy the self-energy of an isolated elementary Pitaevskii vortex, for the first time.

Keywords

Cite

@article{arxiv.2208.10412,
  title  = {Hamiltonian derivation of the point vortex model from the two-dimensional nonlinear Schr\"odinger equation},
  author = {Jonathan Skipp and Jason Laurie and Sergey Nazarenko},
  journal= {arXiv preprint arXiv:2208.10412},
  year   = {2023}
}

Comments

7 pages with 2 figures. v3: Accepted for publication