Propagating and annihilating vortex dipoles in the Gross-Pitaevskii equation
| Autor: | Michael E. Fisher, Cecilia Rorai, Katepalli R. Sreenivasan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Quantum fluid
Physics Fluid Dynamics (physics.flu-dyn) Quantum vortex FOS: Physical sciences Physics - Fluid Dynamics Condensed Matter Physics Space (mathematics) Electronic Optical and Magnetic Materials Vortex Gross–Pitaevskii equation Dipole Quantum Gases (cond-mat.quant-gas) Quantum mechanics Wave function Condensed Matter - Quantum Gases Superfluid helium-4 |
| Popis: | Quantum vortex dynamics in Bose-Einstein condensates or superfluid helium can be informatively described by the Gross-Pitaevskii (GP) equation. Various approximate analytical formulas for a single stationary vortex are recalled and their shortcomings demonstrated. Significantly more accurate two-point [2/2] and [3/3] Pad\'e approximants for stationary vortex profiles are presented. Two straight, singly quantized, antiparallel vortices, located at a distance ${d}_{0}$ apart, form a vortex dipole, which, in the GP model, can either annihilate $or$ propagate indefinitely as a ``solitary wave.'' We show, through calculations performed in a periodic domain, that the details and types of behavior displayed by vortex dipoles depend strongly on the initial conditions rather than only on the separation distance ${d}_{0}$ (as has been previously claimed). It is found, indeed, that the choice of the initial two-vortex profile (i.e., the modulus of the ``effective wave function''), strongly affects the vortex trajectories and the time scale of the process: annihilation proceeds more rapidly when low-energy (or ``relaxed'') initial profiles are imposed. The initial ``circular'' phase distribution contours, customarily obtained by multiplying an effective wave function for each individual vortex, can be generalized to explicit elliptical forms specified by two parameters; then by ``tuning'' the elliptical shape at fixed ${d}_{0}$, a sharp transition between solitary-wave propagation and annihilation is captured. Thereby, a ``phase diagram'' for this ``AnSol'' transition is constructed in the space of ellipticity and separation and various limiting forms of the boundary are discussed. |
| Databáze: | OpenAIRE |
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