Hydrodynamics of vortices in Bose-Einstein condensates: A defect-gauge field approach

Abstract

This work rectifies the hydrodynamic equations commonly used to describe the superfluid velocity field in such a way that vortex dynamics are also taken into account. In the field of quantum turbulence, it is of fundamental importance to know the correct form of the equations which play similar roles to the Navier-Stokes equation in classical turbulence. Here, such equations are obtained by carefully taking into account the frequently overlooked multivalued nature of the $U(1)$ phase field. Such an approach provides exact analytical explanations to some numerically observed features involving the dynamics of quantum vortices in Bose-Einstein condensates, such as the universal $t^{1/2}$ behavior of reconnecting vortex lines. It also expands these results beyond the Gross-Pitaevskii theory so that some features can be generalized to other systems such as superfluid ${}^4$He, dipolar condensates, and mixtures of different superfluid systems.

6 pages, 2 figures

References in corpus (5)

• Emergence of turbulence in an oscillating Bose-Einstein condensate
• Introduction to quantum turbulence
• Inverse Energy Cascade in Forced 2D Quantum Turbulence
• Vortex-boson duality in four space-time dimensions
• The internal structure of a vortex in a two-dimensional superfluid with long healing length and its implications

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• On the finite-size effects in two segregated Bose-Einstein condensates restricted by a hard wall
• A method for the dynamics of vortices in a Bose-Einstein condensate: analytical equations of the trajectories of phase singularities
• Incompressible Energy Spectrum from Wave Turbulence
• Dynamics of Polar-Core Spin Vortices in Inhomogeneous Spin-1 Bose-Einstein Condensates