Dynamics of Vortex Dipoles in Confined Bose-Einstein Condensates

TL;DR

This paper provides a comprehensive theoretical study of the motion, stability, and integrability of vortex dipoles in confined Bose-Einstein condensates, revealing their equilibrium states and dynamic behaviors.

Contribution

It introduces a new dynamical model for vortex dipoles, analyzes their integrability, and characterizes their stationary and rotating equilibria within trapped condensates.

Findings

Identification of conserved quantities in vortex dynamics

Existence of stationary and rotating equilibrium solutions

Classification of vortex motion as quasi-periodic

Abstract

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.