Bifurcations in Attractive Bose-Einstein Condensates and Superfluid Helium

  • Cristián Huepe
  • Caroline Nore
  • Marc-Etienne Brachet
Conference paper
Part of the Nonlinear Phenomena and Complex Systems book series (NOPH, volume 8)


We consider systems containing a Bose-Einstein condensate described by a macroscopic wave function that obeys a Nonlinear Schrödinger like equation (NLSE). Using a continuation method, we characterize the bifurcation of stationary states.

For attractive Bose condensates confined in isotropic potentials, we show the presence of an Hamiltonian saddle-node bifurcation where the stable (elliptic) and unstable (hyperbolic) solutions meet. The condensate decay rates corresponding to macroscopic quantum tunnelling, thermal fluctuations and inelastic collisions are determined. The influence of anisotropy on the bifurcation diagram is also characterised. This requires three-dimensional computations.

For two-dimensional superflows past a cylinder, we also find a saddle-node bifurcation. Through a secondary pitchfork bifurcation, the unstable branch generates one-vortex asymmetric fields that are the nucleation solutions. We characterize on the bifurcation diagram the influence of the ratio of the coherence length to the disc diameter. A study of the system’s three-dimensional instabilities is carried out. We demonstrate that vortex stretching can be induced at subcritical velocities.


Bifurcation Diagram Critical Velocity Vortex Line Gaussian Approximation Bose Condensate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Cristián Huepe
    • 1
  • Caroline Nore
    • 2
  • Marc-Etienne Brachet
    • 1
  1. 1.Laboratoire de Physique Statistique de l’Ecole Normale Supérieure associé au CNRSUniversités Paris 6 et 7ParisFrance
  2. 2.LIMSIUniversité de Paris-SudOrsay CedexFrance

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