| Recently considerable attention has been paid to the description of decay, scattering and transport behaviour of Bose-Einstein condensates phenomenologically described by effective non-Hermitian mean-field theories. However, a derivation of a mean-field approximation starting from a non-Hermitian many-particle system has hitherto been missing. In the present talk we provide such a derivation for an open two-mode Bose-Hubbard dimer, which serves as a model for a BEC in a leaking double-well trap. Starting from the dynamics of operators, we derive a non-Hermitian mean-field description. The resulting nonlinear, non-Hermitian two-level dynamics, in particular the fixed point structures showing characteristic modifications of the self trapping transition, are analysed. The mean-field dynamics is found to be in reasonable agreement with the full many-particle evolution. |
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