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The boson-Hubbard dimer describes a BEC in a double well potential, using
the two mode approximation which is relevant in the weak tunneling regime.
Analytical expressions for the energy eigenstates of this model are obtained by applying perturbation theory in the small tunneling amplitude limit. They are compared with the corresponding numerical solutions and the limits of their validity are determined. These results are used for calculating the time evolution of the number difference of bosons between the two sites of the dimer. The analytical formulas concerning the time dependence of this observable for different initial conditions (completely localized states and coherent spin states) are compared with direct numerical solutions of the quantum system, as well as with the corresponding Gross-Pitaevskii (i.e. mean-field) dynamics. References: [1] Phys. Rev. A 65, 043616 (2002) [2] Phys. Rev. A 68, 023602 (2003) [3] J. Phys. B 36, 3233 (2003) Collaborators: A.R. Bishop, Los Alamos National Lab. |