Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

TL;DR

This paper analyzes the complex dynamics of vortex dipoles in anisotropic Bose-Einstein condensates using reduced models, revealing stochastic reversals, chaotic trajectories, and constructing complex periodic orbits consistent with the full condensate model.

Contribution

It introduces a simplified dynamical system for vortex dipoles in anisotropic traps and uncovers new regimes including stochastic reversals and chaos, supported by numerical and analytical methods.

Findings

Identification of pendulum-like dynamics near guiding centers

Discovery of stochastic reversals in vortex rotation

Construction of complex periodic orbits in the original PDE model

Abstract

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system we are able to construct complex periodic orbits in the original, partial differential equation, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations.