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Dynamical Laws of the Coupled Gross-Pitaevskii Equations for Spin-1 Bose-Einstein Condensates
Methods and Applications of Analysis
  • Weizhu Bao
  • Yanzhi Zhang, Missouri University of Science and Technology

In this paper, we derive analytically the dynamical laws of the coupled Gross- Pitaevskii equations (CGPEs) without/with an angular momentum rotation term and an external magnetic field for modelling nonrotating/rotating spin-1 Bose-Eintein condensates. We prove the conservation of the angular momentum expectation when the external trapping potential is radially symmetric in two dimensions and cylindrically symmetric in three dimensions; obtain a system of first order ordinary differential equations (ODEs) governing the dynamics of the density of each component and solve the ODEs analytically in a few cases; derive a second order ODE for the dynamics of the condensate width and show that it is a periodic function without/with a perturbation; construct the analytical solution of the CGPEs when the initial data is chosen as a stationary state with its center- of-mass shifted away from the external trap center. Finally, these dynamical laws are confirmed by the direct numerical simulation results of the CGPEs.

Mathematics and Statistics
Keywords and Phrases
  • Rotating spin-1 Bose-Einstein condensate,
  • Coupled Gross-Pitaevskii equations,
  • Angular momentum rotation,
  • Condensate width,
  • Angular momentum expectation
Document Type
Article - Journal
Document Version
File Type
© 2010 International Press, All rights reserved.
Publication Date
Citation Information
Weizhu Bao and Yanzhi Zhang. "Dynamical Laws of the Coupled Gross-Pitaevskii Equations for Spin-1 Bose-Einstein Condensates" Methods and Applications of Analysis Vol. 17 Iss. 1 (2010) p. 49 - 80 ISSN: 1073-2772
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