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Analytical solution of a double-well Bose-Einstein Condensate

We introduce a microscopic computation which shows that the Hamiltonian of a Bose-Einstein Condensate can be analytically solved in the two-mode approximation, in particular, in the case of an asymmetric double-well condensate in the dilute regime. Our model is exactly diagonalisable when the overlap of the quasilocalized modes in each well is small enough with respect to the trap asymmetry. For larger overlaps or highly symmetric traps, our diagonalisable Hamiltonian acquires extra terms that we treat within perturbation theory.