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

Abstract

Various widely-used mean-field type theoriesfor a dilute Bose gas are critically examinedin the light of the recent discovery of Bose-Einsteincondensation 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 statesand the circulating current density in a vortexcorresponding to various levels of mean-field theories are predicted.