# Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates

## TL;DR

This paper derives an exact nonlinear solution for vortex precession in Bose-Einstein condensates within the Lowest Landau Level approximation, offering new analytical insights and predictions for vortex dynamics in weakly interacting regimes.

## Contribution

It presents the first fully nonlinear analytic solution for vortex precession in BECs under the LLL approximation, advancing theoretical understanding of vortex dynamics.

## Key findings

- Analytic solution for vortex precession trajectories
- Prediction of vortex motion in weakly interacting BECs
- Potential for experimental verification and multi-vortex solutions

## Abstract

The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of Bose-Einstein Condensates (BEC) in two-dimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our work provides the first controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multi-vortex solutions.