| The mean-field description of many-boson systems can be formulated as the effective dynamics resulting from a restriction to fully condensed states. For Hermitian systems of weakly interacting particles this yields the Gross-Pitaevskii equation for the dynamics of the effective single-particle wave function. Here we address the question how the mean-field description is modified in the presence of an anti-Hermitian term in the many-particle Hamiltonian. We consider a non-Hermitian Bose-Hubbard dimer, which serves as a model for a BEC in a leaking double-well trap. We show that the mean-field equations of motion can be obtained from a generalised canonical structure including a metric gradient flow. The interplay of nonlinearity and non-Hermiticity introduces a qualitatively new behaviour to the mean- field dynamics: The presence of the non-Hermiticity promotes the so-called self-trapping transition, while damping the self-trapping oscillations, and the nonlinearity introduces a strong sensitivity to the initial conditions in the decay of the normalisation. The full many-particle dynamics shows a rich variety of breakdown and revival, as well as tunnelling phenomena on top of the mean-field structure. |
|