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Hydrodynamics of a quantum vortex in the presence of twist

Published online by Cambridge University Press:  12 October 2020

Matteo Foresti  and
Renzo L. Ricca Open the ORCID record for Renzo L. Ricca [Opens in a new window]
Matteo Foresti
Affiliation:
Department of Mathematics and Applications, University of Milano-Bicocca, Via Cozzi 55, 20125Milano, Italy
Renzo L. Ricca*
Affiliation:
Department of Mathematics and Applications, University of Milano-Bicocca, Via Cozzi 55, 20125Milano, Italy BDIC, Beijing U. Technology, 100 Pingleyuan, Beijing100124, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The equations governing the evolution of quantum vortex defects subject to twist are derived in standard hydrodynamic form. Vortex defects emerge as solutions of the Gross–Pitaevskii equation, that by Madelung transformation admits a hydrodynamic description. Here, we consider a vortex defect subject to superposed twist due to the rotation of the phase of the wave function. We prove that, when twist is present, the corresponding Hamiltonian is non-Hermitian and determine the effect of twist on the energy expectation value of the system. We show how twist diffusion may trigger linear instability, a property directly related to the non-Hermiticity of the Hamiltonian. We derive the correct continuity equation and, by applying defect theory, we obtain the correct momentum equation. Finally, by coupling twist kinematics and vortex dynamics we determine the full set of hydrodynamic equations governing quantum vortex evolution subject to twist.

JFM classification

Complex Fluids: Quantum fluids Mathematical Foundations: Topological fluid dynamics Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A25
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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