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On the zero helicity condition for quantum vortex defects

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Abstract In this note we provide an analytical proof of the zero helicity condition for systems governed by the Gross–Pitaevskii equation (GPE). The proof is based on the hydrodynamic interpretation… Click to show full abstract

Abstract In this note we provide an analytical proof of the zero helicity condition for systems governed by the Gross–Pitaevskii equation (GPE). The proof is based on the hydrodynamic interpretation of the GPE, and the direct use of Noether's theorem by applying Kleinert's multi-valued gauge theory. As a by-product we also demonstrate the conservation and quantization of the circulation for the GPE.

Keywords: zero helicity; helicity condition; quantum vortex; condition quantum

Journal Title: Journal of Fluid Mechanics
Year Published: 2023

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