A Vortex Filament Tracking Method for the Gross-Pitaevskii Model of a Superfluid
arXiv:1604.03595 · doi:10.1088/1751-8113/49/41/415502
Abstract
We present an accurate and robust numerical method to track quantized vortex lines in a superfluid described by the Gross-Pitaevskii equation. By utilizing the pseudo-vorticity field of the associated complex scalar order parameter of the superfluid, we are able to track the topological defects of the superfluid and reconstruct the vortex lines which correspond to zeros of the field. Throughout, we assume our field is periodic to allow us to make extensive use of the Fourier representation of the field and its derivatives in order to retain spectral accuracy. We present several case studies to test the precision of the method which include the evaluation of the curvature and torsion of a torus vortex knot, and the measurement of the Kelvin wave spectrum of a vortex line and a vortex ring. The method we present makes no a-priori assumptions on the geometry of the vortices and is therefore applicable to a wide range of systems such as a superfluid in a turbulent state that is characterised by many vortex rings coexisting with sound waves. This allows us to track the positions of the vortex filaments in a dense turbulent vortex tangle and extract statistical information about the distribution of the size of the vortex rings and the inter-vortex separations. In principle, the method can be extended to track similar topological defects arising in other physical systems.
arXiv comment22 pages, 8 figures
References in corpus (34)
- Kelvin Wave Cascade and Decay of Superfluid Turbulence
- A Kelvin-wave cascade on a vortex in superfluid He at a very low temperature
- Quantum vortex reconnections
- How superfluid vortex knots untie
- Wave turbulence and vortices in Bose-Einstein condensation
- Helicity conservation by flow across scales in reconnecting vortex links and knots
- Pade approximations of solitary wave solutions of the Gross-Pitaevskii equation
- Vortex knots in a Bose-Einstein condensate
- Superfluid turbulence from quantum Kelvin wave to classical Kolmogorov cascades
- Spectrum of Kelvin-wave turbulence in superfluids
- Theory of decay of superfluid turbulence in the low-temperature limit
- Energy cascade with small-scales thermalization, counterflow metastability and anomalous velocity of vortex rings in Fourier-truncated Gross-Pitaevskii equation
- Creation and characterization of vortex clusters in atomic Bose-Einstein condensates
- Vortex pairing in two-dimensional Bose gases
- Structure of quantum vortex tangle in He-4 counterflow turbulence
- Kelvin-wave cascade and dissipation in low-temperature superfluids vortices
- Breathers on Quantized Superfluid Vortices
- Velocity, energy and helicity of vortex knots and unknots
- Helicity, Topology and Kelvin Waves in reconnecting quantum knots
- Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence
- Derivation of the Biot-Savart equation from the Nonlinear Schrödinger equation
- Interactions of vortices with rarefaction solitary waves in a Bose-Einstein condensate and their role in the decay of superfluid turbulence
- Helicity conservation under quantum reconnection of vortex rings
- Spatio-temporal detection of Kelvin waves in quantum turbulence simulations
- Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation
- A lattice QCD study of generalized gluelumps
- Geometry and scaling of tangled vortex lines in three-dimensional random wave fields
- Classical-like wakes past elliptical obstacles in atomic Bose-Einstein condensates
- Energy spectrum of the 3D velocity field, induced by vortex tangle
- Torus quantum vortex knots in the Gross-Pitaevskii model for Bose-Einstein condensates
- Scattering of Line-Ring Vortices in a Superfluid
- Interaction and decay of Kelvin waves in the Gross-Pitaevskii model
- Approach and separation of quantum vortices with balanced cores
- Helicity within the vortex filament model
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- Vortex reconnections and rebounds in trapped atomic Bose--Einstein condensates
- (Non)-universality of vortex reconnections in superfluids
- Critical transport and vortex dynamics in a thin atomic Josephson junction
- Vortex motion quantifies strong dissipation in a holographic superfluid
- Irreversible dynamics of vortex reconnections in quantum fluids
- Rotating quantum turbulence in the unitary Fermi gas
- Interaction between active particles and quantum vortices leading to Kelvin wave generation
- Vorticity and quantum turbulence in the merging of superfluid Helium nanodroplets
- Dynamical Phase Diagram of Ultracold Josephson Junctions
- Dissipative Dynamics of Quantum Vortices in Fermionic Superfluid
- Separation scaling for viscous vortex reconnection
- Universal Aspects of Vortex Reconnections across the BCS-BEC Crossover
- Quasi-stable quantum vortex knots and links in anisotropic harmonically trapped Bose-Einstein condensates
- Breaking of Josephson junction oscillations and onset of quantum turbulence in Bose--Einstein condensates
- A matching theory to characterize sound emission during vortex reconnection in quantum fluids
- Relaxation dynamics of half-quantum vortices in a two-dimensional two-component Bose-Einstein condensate
- Dynamics of a Vortex Dipole in a Holographic Superfluid
- Active and finite-size particles in decaying quantum turbulence at low temperature
- Spin-up of a superfluid vortex lattice driven by rough boundaries
- Quantum vortex reconnections mediated by trapped particles
- Vortex-loop calculation of the specific heat of superfluid He under pressure
- Simulating Quantum Turbulence with Matrix Product States
- Numerical simulation of the Gross-Pitaevskii equation via vortex tracking
- Crow instability of vortex lines in dipolar superfluids
- Controlled generation of 3D vortices in driven atomic Josephson junctions
- Spontaneous Quantum Turbulence in a Newborn Bose-Einstein Condensate via the Kibble-Zurek Mechanism
- Merging of superfluid Helium nanodroplets with vortices