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Title: Analytical and numerical studies of Bose - Einstein condensates
Keywords: Bose-Einstein condensation, Gross-Pitaevskii equation, asymptotic approximation, normalized gradient flow, spinor condensates, optical lattice
Issue Date: 20-Mar-2009
Source: LIM FONG YIN (2009-03-20). Analytical and numerical studies of Bose - Einstein condensates. ScholarBank@NUS Repository.
Abstract: This thesis presents the analytical and numerical studies of Bose-Einstein condensates (BECs) in cold dilute atomic gases, within the description of the mean field theory and the Gross-Pitaevskii equation (GPE). The ground state of a single component BEC confined in external potential is studied analytically through asymptotic approximation, in both strongly repulsively and strongly attractively interacting regimes. Symmetry breaking of a weakly attractively interacting BEC confined in a one-dimensional double well potential is also studied. In numerical study, the normalized gradient flow method utilized with the sine-pseudospectral method is introduced to solve the GPE for the ground state effectively. The method is then extended to spin-1 BEC which is described by three-component coupled GPEs. Finally, a study on the transport of a strongly repulsively interacting BEC through a shallow optical lattice of finite width is presented. A dynamical self-trapped state is observed and it can be explained by the nonlinear band structure in a periodic potential.
Appears in Collections:Ph.D Theses (Open)

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