Motion of a vortex line near the boundary of a semi-infinite uniform condensate

TL;DR

This paper analyzes the motion of a vortex near a boundary in a condensate, revealing how the boundary affects vortex dynamics through an image vortex analogy and an effective shift related to the healing length.

Contribution

It introduces a modified vortex motion model near a boundary, accounting for the surface layer effects and deriving an approximate velocity formula involving the healing length.

Findings

Vortex velocity is approximated by U ≈ (ħ/2m)(y₀ - √2 ξ)⁻¹.

Surface layer causes an effective shift in the image vortex position.

Boundary effects significantly influence vortex dynamics in condensates.

Abstract

We consider the motion of a vortex in an asymptotically homogeneous condensate bounded by a solid wall where the wave function of the condensate vanishes. For a vortex parallel to the wall, the motion is essentially equivalent to that generated by an image vortex, but the depleted surface layer induces an effective shift in the position of the image compared to the case of a vortex pair in an otherwise uniform flow. Specifically, the velocity of the vortex can be approximated by $U \approx (\hbar/2m)(y_0-\sqrt 2 \xi)^{-1}$, where $y_0$ is the distance from the center of the vortex to the wall, $\xi$ is the healing length of the condensate and $m$ is the mass of the boson.