| The celebrated meanfield approximation for Bose-Einstein condensates can be interpreted as a classical limit of a full many particle description, where the inverse of the particle number is related to an effecitve hbar. To clarify the validity of this analogy, we study an N-particle, two-mode Bose-Hubbard system, modelling a Bose-Einstein condensate in a double-well potential. We investigate the correspondence of the full many particle description and the meanfield approximation. Furthermore we introduce a semiclassical approximation based on the classical dynamics of the meanfield Gross-Pitaevskii equation, which allows an approximate reconstruction of the quantum properties of the N particle system, e.g. the eigenvalues and eigenfunctions, using a WKB type quantization condition. |
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