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Abstract

We explore the topological transformation of quasi-2D Bose-Einstein condensates of dilute atomic gases, and changes in the collective modes as the confining potential is modified from rotationally symmetric multiply connected to multiply connected with broken rotational symmetry and ultimately to a simply connected geometry. In particular, we show that the condensate density, and the non-condensate density arising from the quantum fluctuations, follow the transition in the geometry of the confining potential. The non-condensate density arising from the thermal fluctuations, in contrast, remain multiply connected when the thermal energy exceeds the maximum value in the basin of the confining potential. Otherwise, both the condensate and non-condensate densities become simply connected. The topology of the non-condensate densities is determined by the thermal energy, the repulsive interaction energy between atoms, and the trapping potential energy. In particular, the origin of the difference lies in the structure of the low-energy collective modes, which we examine using the Hartree-Fock-Bogoliubov formalism. We then use the Hartree-Fock-Bogoliubov theory with the Popov approximation to investigate the density and the momentum distribution associated with the thermal fluctuations.