Dynamics of inertial vortices in multi-component Bose-Einstein condensates

TL;DR

This paper investigates the nonlinear dynamics of multi-component Bose-Einstein condensates with vortices, revealing inertial effects and complex interactions that differ from classical vortex theories, including chaotic behavior in vortex systems.

Contribution

It introduces an effective nonlinear vortex core dynamics with inertia in multi-component BECs, contrasting with traditional point vortex models, and explores vortex interactions and chaos.

Findings

Vortex cores behave as inertial particles with effective nonlinear dynamics.

Vortex-vortex interactions are short-ranged and repulsive, decreasing with distance.

Chaotic behavior observed in three-vortex systems due to inertia.

Abstract

With use of the nonlinear Schr{\"o}dinger (or Gross-Pitaevskii) equation with strong repulsive cubic nonlinearity, dynamics of multi-component Bose-Einstein condensates (BECs) with a harmonic trap in 2 dimensions is investigated beyond the Thomas-Fermi regime. In the case when each component has a single vortex, we obtain an effective nonlinear dynamics for vortex cores (particles). The particles here acquire the inertia, in marked contrast to the standard theory of point vortices widely known in the usual hydrodynamics. The effective dynamics is equivalent to that of charged particles under a strong spring force and in the presence of Lorentz force with the uniform magnetic field. The inter-particle (vortex-vortex) interaction is singularly-repulsive and short-ranged with its magnitude decreasing with increasing distance of the center of mass from the trapping center. "Chaos in the three-body problem" in the three vortices system can be seen, which is not expected in the corresponding point vortices without inertia in 2 dimensions.