Bose-Einstein Condensation in a Confined Geometry with and without a Vortex

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Abstract
Various widely-used mean-field type theories for a dilute Bose gas are critically examined in the light of the recent discovery of Bose-Einstein condensation of atomic gases in a confined geometry. By numerically solving the mean-field equations within the framework of the Bogoliubov approximation both stationary non-uniform case and the vortex case under rotation in a cylindrically symmetric vessel are investigated. We obtain spatial structures of condensate, non-condensate, anomalous correlation. The low lying excitation spectra, the local density of states and the circulating current density in a vortex corresponding to various levels of mean-field theories are predicted.Comment: 16 pages, LaTeX with jpsj.sty, 13 eps figures. Figures improve