Quantized vortices are phase singularities in complex fields. In superfluids, they appear as mobile interacting defects that may cross and reconnect by exchanging tails. Reconnection is a topology-changing event that allows vortex tangles to decay; it is a defining signature of quantum turbulence. We report a family of fixed points (i.e., stationary solutions), including planar forms, that capture reconnection in the Gross-Pitaevskii model in contrast to previous suggestions of pyramidal structures. These are obtained using a well known, systematic method for generating low-energy relaxed initial conditions for Gross-Pitaevskii simulations.
Quantized vortices are phase singularities in complex fields. In superfluids, they appear as mobile interacting defects that may cross and reconnect by exchanging tails. Reconnection is a topology-changing event that allows vortex tangles to decay; it is a defining signature of quantum turbulence. We report a family of fixed points (i.e., stationary solutions), including planar forms, that capture reconnection in the Gross-Pitaevskii model in contrast to previous suggestions of pyramidal structures. These are obtained using a well known, systematic method for generating low-energy relaxed initial conditions for Gross-Pitaevskii simulations.
We study numerically the reconnection of quantized vortices and the concurrent acoustic emission by the analysis of the Gross-Pitaevskii equation. Two quantized vortices reconnect following the process similar to classical vortices; they approach, twist themselves locally so that they become anti-parallel at the closest place, reconnect and leave separately.The investigation of the motion of the singular lines where the amplitude of the wave function vanishes in the vortex cores confirms that they follow the above scenario by reconnecting at a point. This reconnection is not contradictory to the Kelvin's circulation theorem, because the potential of the superflow field becomes undefined at the reconnection point. When the locally anti-parallel part of the vortices becomes closer than the healing length, it moves with the velocity comparable to the sound velocity, emits the sound waves and leads to the pair annihilation or reconnection; this phenomena is concerned with the Cherenkov resonance. The vortices are broken up to smaller vortex loops through a series of reconnection, eventually disappearing with the acoustic emission. This may correspond to the final stage of the vortex cascade process proposed by Feynman. The change in energy components, such as the quantum, the compressible and incompressible kinetic energy is analyzed for each dynamics. The propagation of the sound waves not only appears in the profile of the amplitude of the wave function but also affects the field of its phase, transforming the quantum energy due to the vortex cores to the kinetic energy of the phase field.
A quantum vortex is a topological singularity with quantized circulation, unlike a classical vortex with its continuous circulation strength.Quantum turbulence, envisaged as strong tangle of quantum vortices, of a Bose-Einstein condensate is examined by developing a unitary qubit lattice algorithm for the solution of the Gross-Pitaevskii equation.Earlier, it was shown that a certain class of initial conditions had a very short Poincare recurrence time for this Hamiltonian system.Here it is shown quantitatively that increasing the internal energy of the initial state leads to a systematic degradation of this class of solutions.Coupled Bose-Einstein condensate systems are investigated for a Hopf link class of initial conditions in which a vortex ring core is threaded by a linear vortex core that then closes toroidal around the vortex ring.These states are known as skyrmions and play a role in particle physics, astrophysics and condensed matter physics.
The scaling laws for the reconnection of isolated pairs of quantised vortices are characterised by numerically integrating the three-dimensional Gross–Pitaevskii equations, the simplest mean-field equations for a quantum fluid. The primary result is the identification of distinctly different temporal power laws for the pre- and post-reconnection separation distances $\unicode[STIX]{x1D6FF}(t)$ for two configurations. For the initially anti-parallel case, the scaling laws before and after the reconnection time tr obey the dimensional $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/2}$ prediction with temporal symmetry about tr and physical space symmetry about the mid-point between the vortices xr . The extensions of the vortex lines close to reconnection form the edges of an equilateral pyramid. For all of the initially orthogonal cases, $\unicode[STIX]{x1D6FF}\sim |t_{r}-t|^{1/3}$ before reconnection and $\unicode[STIX]{x1D6FF}\sim |t-t_{r}|^{2/3}$ after reconnection are respectively slower and faster than the dimensional prediction. For both configurations, smooth scaling laws are generated due to two innovations. The first innovation is to use an initial low-energy vortex-core density profile that suppresses unwanted density fluctuations as the vortices evolve in time. The other innovation is the accurate identification of the position of the vortex cores from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories allow us to calculate the Frenet–Serret frames and the curvature of the vortex lines, secondary results that might hold clues for the origin of the differences between the scaling laws of the two configurations. Reconnection takes place in a reconnection plane defined by the average tangents Tav and curvature normal Nav directions of the pseudo-vorticity curves at the points of closest approach, at time t≈tr . To characterise the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, from which four angles $\unicode[STIX]{x1D703}_{i}$ between the lines are defined. Their sum is convex or hyperbolic, that is $\sum _{i=1,4}\unicode[STIX]{x1D703}_{i}>360^{\circ }$ , for the orthogonal cases, as opposed to the acute angles of the pyramid found for the anti-parallel initial conditions.
Vortex reconnections are fundamental events in fluid motion, randomizing the velocity field, changing the topology, and redistributing energy across length scales. In superfluid helium and atomic Bose–Einstein condensates, vortices are effectively one-dimensional lines called quantum vortices (akin to minitornadoes of a fixed strength). Individual reconnections happen when two vortices collide and subsequently recoil, exchanging heads and tails. Recent experimental progress opens the possibility of answering the important question as to whether reconnections obey a universal behavior. Here we show that the intervortex distance between reconnecting vortices obeys two fundamental scaling laws, which we identify in experimental data and numerical simulations, across homogeneous superfluids and trapped condensates.
Reconnections between quantum vortex filaments in the presence of trapped particles are investigated using numerical simulations of the Gross-Pitaevskii equation. Particles are described with classical degrees of freedom and modeled as highly repulsive potentials which deplete the superfluid. First, the case of a vortex dipole with a single particle trapped inside one of the vortices is studied. It is shown that the reconnection takes place at the position of the particle as a consequence of the symmetry breaking induced by it. The separation rate between the reconnecting points is compatible with the known dynamics of quantum vortex reconnections, and it is independent of the particle mass and size. After the reconnection, the particle is pushed away with a constant velocity, and its trajectory is deflected because of the transverse momentum exchange with the vortex filaments. The momentum exchanges between the particle, the vortex, and a density pulse are characterized. Finally, the reconnection of two linked rings, each of them with several initially randomly distributed particles, is studied. It is observed that generically, reconnections take place at the location of trapped particles. It is shown that reconnection dynamics is unaffected for light particles.
Using two innovations, smooth, but distinctly different, scaling laws for the numerical reconnection of pairs of initially orthogonal and anti-parallel quantum vortices are obtained using the three-dimensional Gross-Pitaevskii equations, the simplest mean-field non-linear Schrödinger equation for a quantum fluid. The first innovation suppresses temporal fluctuations by using an initial density profile that is slightly below the usual two-dimensional steady-state Padé approximate profiles. The second innovation is to find the trajectories of the quantum vortices from a pseudo-vorticity constructed on the three-dimensional grid from the gradients of the wave function. These trajectories then allow one to calculate the Frenet-Serret frames and the curvature of the vortex lines. For the anti-parallel case, the scaling laws just before and after reconnection obey the dimensional δ∼∣tr−t∣1/2 prediction with temporal symmetry about the reconnection time tr and physical space symmetry about the xr, the mid-point between the vortices, with extensions of the vortex lines formng the edges of an equilateral pyramid. For all of the orthogonal cases, before reconnection δin∼(t−tr)1/3 and after reconnection δout∼(t−tr)2/3, which are respectively slower and faster than the dimensional prediction. In these cases, the reconnection takes place in a plane defined by the directions of the curvature and vorticity. To define the structure further, lines are drawn that connect the four arms that extend from the reconnection plane, four angles θi between these arms are found, then summed, giving ∑θi>360∘. This implies that the overall structure is convex or hyperbolic, as opposed to the acute angles of the anti-parallel pyramid.