Journal of Low Temperature Physics

, Volume 191, Issue 3–4, pp 242–256 | Cite as

Kinematics of the Doped Quantum Vortices in Superfluid Helium Droplets

  • Charles Bernando
  • Andrey F. Vilesov


Recent observation of quantum vortices in superfluid \(^{4}\)He droplets measuring a few hundreds of nanometers in diameter involved decoration of vortex cores by clusters containing large numbers of Xe atoms, which served as X-ray contrast agents. Here, we report on the study of the kinematics of the combined vortex–cluster system in a cylinder and in a sphere. Equilibrium states, characterized by total angular momentum, L, were found by minimizing the total energy, E, which sums from the kinetic energy of the liquid due to the vortex and due to orbiting Xe clusters, as well as solvation energy of the cluster in the droplet. Calculations show that, at small mass of the cluster, the equilibrium displacement of the system from the rotation axis is close to that for the bare vortex. However, upon decrease in L beyond certain critical value, which is larger for heavier clusters, the displacement bifurcates toward the surface region, where the motion of the system is governed by the clusters. In addition, at even smaller L, bare orbiting clusters become energetically favorable, opening the possibility for the vortex to detach from the cluster and to annihilate at the droplet’s surface.


quantum vortices Superfluidity Helium droplets 



This work was supported by the NSF Grants DMR-1501276 and DMR-1701077. The authors are thankful to Dr. Curtis Jones for his early contributions to this work and to Sean O’Connell, Rico Mayro Tanyag and Deepak Verma, for careful reading of the manuscript.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of ChemistryUniversity of Southern CaliforniaLos AngelesUSA

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