Analytical solutions of the Bogoliubov-de Gennes equations for excitations of a trapped Bose-Einstein-condensed gas

Journal Article · Tue Jun 01 00:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.063608· OSTI ID:20643802

Bambi, Hu ^[1]; Guoxiang, Huang ^[1]; Yongli, Ma ^[1]

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1. Department of Physics and the Center for Nonlinear Studies, Hong Kong Baptist University, Hong Kong (China)

We propose a method for finding analytical solutions of the Bogoliubov-de Gennes (BdG) equations for the low-lying collective excitations in a harmonically trapped Bose-Einstein condensate beyond the Thomas-Fermi limit. We first use a simple variational wave function for ground state to eliminate the divergence at the boundary layer of the condensate, which appears in the Thomas-Fermi approximation. We then solve the BdG equations analytically and obtain explicit and divergence-free expressions for the eigenvalues and eigenfunctions of the excitations for the traps with spherical and cylindrical symmetries. The solutions of the zero-energy mode of the BdG equations are also presented.

• OSTI ID: 20643802
• Journal Information: Physical Review. A, Vol. 69, Issue 6; Other Information: DOI: 10.1103/PhysRevA.69.063608; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ANALYTICAL SOLUTION
BOSE-EINSTEIN CONDENSATION
BOSONS
BOUNDARY LAYERS
COLLECTIVE EXCITATIONS
CYLINDRICAL CONFIGURATION
EIGENFUNCTIONS
EIGENVALUES
GROUND STATES
QUANTUM MECHANICS
SPHERICAL CONFIGURATION
SYMMETRY
THOMAS-FERMI MODEL
TRAPPING
TRAPS
VARIATIONAL METHODS
WAVE FUNCTIONS