Hamiltonian dynamics of two same-sign point vortices

TL;DR

This study numerically analyzes the Hamiltonian dynamics of two same-sign point vortices in a trapped Bose-Einstein condensate, revealing a phase space wall dividing two distinct vortex orbit types.

Contribution

It identifies a phase space wall that separates two different dynamical behaviors of vortex pairs, a novel finding in vortex dynamics within Bose-Einstein condensates.

Findings

Discovered a phase space wall dividing vortex dynamics into two types.

Characterized the two vortex orbit types in position and velocity space.

Found the phase space wall is distinct from known bifurcation curves.

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)].