Classical analogies for the force acting on an impurity in a Bose-Einstein condensate

Jonas Rønning, Audun Skaugen, Emilio Hernández-García, Cristobal Lopez, Luiza Angheluta

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


We study the hydrodynamic forces acting on a small impurity moving in a two-dimensional Bose-Einstein condensate at non-zero temperature. The condensate is modelled by the damped-Gross Pitaevskii (dGPE) equation and the impurity by a Gaussian repulsive potential coupled to the condensate. For weak coupling, we obtain analytical expressions for the forces acting on the impurity, and compare them with those computed through direct numerical simulations of the dGPE and with the corresponding expressions for classical forces. For non-steady flows, there is a time-dependent force dominated by inertial effects and which has a correspondence in the Maxey-Riley theory for particles in classical fluids. In the steady-state regime, the force is dominated by a self-induced drag. Unlike at zero temperature, where the drag force vanishes below a critical velocity, at low temperatures the impurity experiences a net drag even at small velocities, as a consequence of the energy dissipation through interactions of the condensate with the thermal cloud. This dissipative force due to thermal drag is similar to the classical Stokes' drag. There is still a critical velocity above which steady-state drag is dominated by acoustic excitations and behaves non-monotonically with impurity's speed.

Original languageEnglish
Number of pages14
JournalNew Journal of Physics
Issue number7
Publication statusPublished - 1 Jul 2020
Publication typeA1 Journal article-refereed


  • Bose Einstein condensate
  • fluid dynamics
  • Gross Pitaevskii equation
  • particles in fluids
  • superfluidity

Publication forum classification

  • Publication forum level 2

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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