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An exactly solvable model mimicking demixing of two Bose-Einstein condensatesat the many-body level of theory is devised. Various properties are expressedin closed form along the demixing pathway and investigated. The connectionbetween the center-of-mass coordinate and in particular the relativecenter-of-mass coordinate and demixing is explained. The model is also exactlysolvable at the mean-field level of theory, allowing thereby comparison betweenmany-body and mean-field properties. Applications are briefly discussed.

Effects Beyond Center-of-Mass Separability in a Trapped Bosonic Mixture: Exact Results