Hamiltonian dynamics of two same-sign point vortices
Abstract
We have studied numerically the Hamiltonian dynamics of two same-sign point vortices in an effectively two-dimensional, harmonically trapped Bose-Einstein condensate. We have found in the phase space of the system an impenetrable wall that divides the dynamics into two distinct and exhaustive types. In the two-dimensional position-coordinate space, the first type corresponds to intersecting single-vortex orbits and the second type to orbits that have no points in common. The two types are also easily distinguished in the two-dimensional space spanned by the radial and angular velocities of the vortices: in the first type, both single-vortex orbits are the same simple loop in this two-dimensional space, whereas in the second type the two orbits constitute two nonintersecting loops. The phase-space-dividing wall is distinct from the bifurcation curve of rigidly rotating states found by Navarro et al. [Phys. Rev. Lett. 110, 225301 (2013)].
Cite
@article{arxiv.1512.02809,
title = {Hamiltonian dynamics of two same-sign point vortices},
author = {Anderson V. Murray and Andrew J. Groszek and Pekko Kuopanportti and Tapio Simula},
journal= {arXiv preprint arXiv:1512.02809},
year = {2016}
}
Comments
8 pages, 10 figures; v2 identical in content to the published article