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Our aim is to analyze the various energy functionals appearing in the physicsliterature and describing the behavior of a Bose-Einstein condensate in anoptical lattice. We want to justify the use of some reduced models. For thatpurpose, we will use the semi-classical analysis developed for linear problemsrelated to the Schr\"odinger operator with periodic potential or multiple wellspotentials. We justify, in some asymptotic regimes, the reduction to lowdimensional problems and analyze the reduced problems.

On mathematical models for Bose-Einstein condensates in optical lattices (expanded version)