# Dynamics of quantum vortices in a quasi-two-dimensional Bose-Einstein condensate with two "holes"

## TL;DR

This paper analytically studies the dynamics of quantum vortices in a quasi-two-dimensional Bose-Einstein condensate with two density holes, including effects of inhomogeneity and curvature, using a hydrodynamic and Hamiltonian framework.

## Contribution

It introduces an analytical approach to vortex dynamics in inhomogeneous and curved BECs, extending previous models to include density zeros and shell geometries.

## Key findings

- Analytical velocity field for vortices in inhomogeneous condensates.
- Equations of motion in noncanonical Hamiltonian form.
- Generalization to curved shell geometries.

## Abstract

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.