On the characterization of vortex configurations in the steady rotating Bose--Einstein condensates

TL;DR

This paper compares ODE and PDE models to analyze vortex configurations in rotating Bose-Einstein condensates, identifying stable arrangements and validating the models in the semi-classical limit.

Contribution

It provides a detailed analysis of vortex dynamics using both ODE and PDE models, highlighting their agreement in the large chemical potential regime.

Findings

Good agreement between ODE and PDE models in the semi-classical limit.

Characterization of orbitally stable vortex configurations.

Numerical approximation of PDE model confirms theoretical predictions.

Abstract

Motivated by experiments in atomic Bose-Einstein condensates (BECs), we compare predictions of a system of ordinary differential equations (ODE) for dynamics of one and two individual vortices in the rotating BECs with those of the partial differential equation (PDE). In particular, we characterize orbitally stable vortex configurations in a symmetric harmonic trap due to a cubic repulsive interaction and the steady rotation. The ODE system is analyzed in details and the PDE model is approximated numerically. Good agreement between the two models is established in the semi-classical (Thomas-Fermi) limit that corresponds to the BECs at the large chemical potentials.