Hamiltonian Derivation of the Point Vortex Model from the Two-Dimensional Nonlinear Schrödinger Equation

Jonathan Skipp; Jason Laurie; Sergey Nazarenko

doi:10.1103/PhysRevE.107.025107

Hamiltonian Derivation of the Point Vortex Model from the Two-Dimensional Nonlinear Schrödinger Equation

Jonathan Skipp, Jason Laurie, Sergey Nazarenko

Research output: Contribution to journal › Article › peer-review

Abstract

We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schrödinger 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.

Original language	English
Article number	025107
Number of pages	9
Journal	Physical Review E
Volume	107
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.107.025107
Publication status	Published - 24 Feb 2023

Bibliographical note

This work was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 823937 for the RISE project HALT. J.L. and J.S. are supported by the Leverhulme Trust Project Grant RPG-2021-014.
Copyright ©2023 American Physical Society

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title = "Hamiltonian Derivation of the Point Vortex Model from the Two-Dimensional Nonlinear Schr{\"o}dinger Equation",

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.",

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AB - We present a rigorous derivation of the point vortex model starting from the two-dimensional nonlinear Schrödinger 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.

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Hamiltonian Derivation of the Point Vortex Model from the Two-Dimensional Nonlinear Schrödinger Equation

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