Propagating and annihilating vortex dipoles in the Gross-Pitaevskii equation

Cecilia Rorai, K. R. Sreenivasan, Michael E. Fisher

Research output: Contribution to journalArticlepeer-review


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] Padé approximants for stationary vortex profiles are presented. Two straight, singly quantized, antiparallel vortices, located at a distance d0 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 d0 (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 d0, 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.

Original languageEnglish (US)
Article number134522
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number13
StatePublished - Oct 29 2013

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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