Dynamics of vortices in weakly interacting Bose-Einstein condensates

TL;DR

This paper investigates vortex dynamics in weakly interacting Bose-Einstein condensates using analytical and numerical methods, revealing vortex creation, annihilation, and periodicity loss due to interactions.

Contribution

It introduces a Ritz minimization approach to analyze vortex trajectories and dynamics in Bose-Einstein condensates, highlighting effects of weak interactions.

Findings

Vortex-antivortex pairs can annihilate and re-form under certain conditions.

Additional vortices can be created and annihilated within the condensate.

Periodic vortex behavior persists in noninteracting cases but is disrupted by weak interactions.

Abstract

We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate the trajectories of the vortices. We find conditions under which a vortex-antivortex pair annihilates and is created again. For the case of three vortices we show that at certain times two additional vortices may be created, which move through the condensate and annihilate each other again. For a noninteracting condensate this process is periodic, whereas for small interactions the essential features persist, but the periodicity is lost. The results are compared to exact numerical solutions of the Gross-Pitaevskii equation confirming our analytical findings.