Dynamics of massive point vortices in binary mixture of Bose-Einstein condensates

TL;DR

This paper develops a Lagrangian model for massive point vortices in two-component Bose-Einstein condensates, revealing inertial effects and core mass influence on vortex dynamics, supported by numerical simulations.

Contribution

It derives a Lagrangian for massive vortices using a variational approach, linking vortex inertia to core mass and electromagnetic analogies, and confirms predictions with GP equation simulations.

Findings

Massive vortex cores cause unstable precession.

Small core mass induces radial oscillations.

Numerical results support the inertial vortex model.

Abstract

We study the massive point-vortex model introduced in Ref. [Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.