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.

arXiv comment6 pages, 2 figures

References in corpus (13)

• Emergence of turbulence in an oscillating Bose-Einstein condensate
• Introduction to quantum turbulence
• Kolmogorov spectrum of superfluid turbulence: numerical analysis of the Gross-Pitaevskii equation with the small scale dissipation
• Inverse Energy Cascade in Forced 2D Quantum Turbulence
• Quantum turbulence in trapped atomic Bose-Einstein condensates
• Motion of vortex lines in quantum mechanics
• Reconnection Dynamics for Quantized Vortices
• Vortices near surfaces of Bose-Einstein condensates
• Controlled polarization of two-dimensional quantum turbulence in atomic Bose-Einstein condensates
• 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
• Vortex dynamics in nonrelativistic Abelian Higgs model
• Gauge vortex dynamics at finite mass of bosonic fields

Cited by in corpus (12)

• Motion of vortices in inhomogeneous Bose-Einstein condensates
• Quantum turbulence in quantum gases
• Crossover from interaction to driven regimes in quantum vortex reconnections
• Dynamics of a massive superfluid vortex in $r^k$ confining potentials
• Quantum turbulence in Bose-Einstein condensates: present status and new challenges ahead
• Hydrodynamics of noncircular vortices in beams of light and other two-dimensional fluids
• Thermalized Abrikosov lattices from decaying turbulence in rotating BECs
• Boson-vortex duality in compressible spin-orbit coupled BECs
• On the finite-size effects in two segregated Bose-Einstein condensates restricted by a hard wall
• Incompressible Energy Spectrum from Wave Turbulence
• A method for the dynamics of vortices in a Bose-Einstein condensate: analytical equations of the trajectories of phase singularities
• Dynamics of Polar-Core Spin Vortices in Inhomogeneous Spin-1 Bose-Einstein Condensates