Frontiers of Physics

, Volume 7, Issue 1, pp 54–71 | Cite as

Theory of superfluidity and drag force in the one-dimensional Bose gas

  • Alexander Yu. Cherny
  • Jean-Sébastien Caux
  • Joachim BrandEmail author
Review Article


The one-dimensional Bose gas is an unusual superfluid. In contrast to higher spatial dimensions, the existence of non-classical rotational inertia is not directly linked to the dissipationless motion of infinitesimal impurities. Recently, experimental tests with ultracold atoms have begun and quantitative predictions for the drag force experienced by moving obstacles have become available. This topical review discusses the drag force obtained from linear response theory in relation to Landau’s criterion of superfluidity. Based upon improved analytical and numerical understanding of the dynamical structure factor, results for different obstacle potentials are obtained, including single impurities, optical lattices and random potentials generated from speckle patterns. The dynamical breakdown of superfluidity in random potentials is discussed in relation to Anderson localization and the predicted superfluid-insulator transition in these systems.


Lieb-Liniger model Tonks-Girardeau gas Luttinger liquid drag force superfluidity dynamical structure factor 


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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Yu. Cherny
    • 1
  • Jean-Sébastien Caux
    • 2
  • Joachim Brand
    • 3
    Email author
  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubna, Moscow regionRussia
  2. 2.Institute for Theoretical Physics, Science Park 904University of AmsterdamAmsterdamThe Netherlands
  3. 3.Centre for Theoretical Chemistry and Physics and New Zealand Institute for Advanced StudyMassey UniversityNorth Shore, AucklandNew Zealand

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