Phase Topology of Two Vortices of the Identical Intensities in Bose-Einstein Condensate

TL;DR

This paper analyzes the phase topology of two identical vortices in a Bose-Einstein condensate, revealing a bifurcation of Liouville tori, which connects vortex dynamics to classical rigid body bifurcations.

Contribution

It introduces a Hamiltonian system model for two vortices in a condensate and identifies a novel bifurcation of Liouville tori similar to classical rigid body dynamics.

Findings

Bifurcation of three Liouville tori into one was detected.

The bifurcation resembles that in rigid body dynamics.

The system is a completely integrable Hamiltonian model.

Abstract

Completely Liouville integrable Hamiltonian system with two degrees of freedom, describing the dynamics of two vortex filaments in a Bose-Einstein condensate enclosed in a cylindrical trap, is considered. For the system of two vortices with identical intensities detected bifurcation of three Liouville tori into one. Such a bifurcation was found in the integrable case of Goryachev-Chaplygin-Sretensky in the rigid body dynamics.