Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer - Graefe,E; Korsch,HJ; Niederle,AE (Phys. Rev. A, 2010)
We investigate the many-particle and mean-field correspondence for anon-Hermitian N-particle Bose-Hubbard dimer where a complex onsite energydescribes an effective decay from one of the modes. Recently a generalizedmean-field approximation for this non-Hermitian many-particle system yieldingan alternative complex nonlinear Schr\"odinger equation was introduced. Here wegive details of this mean-field approximation and show that the resultingdynamics can be expressed in a generalized canonical form that includes ametric gradient flow. The interplay of nonlinearity and non-Hermiticityintroduces a qualitatively new behavior to the mean-field dynamics: Thepresence of the non-Hermiticity promotes the self-trapping transition, whiledamping the self-trapping oscillations, and the nonlinearity introduces astrong sensitivity to the initial conditions in the decay of the normalization.Here we present a complete characterization of the mean-field dynamics and thefixed point structure. We also investigate the full many-particle dynamics,which shows a rich variety of breakdown and revival as well as tunnelingphenomena on top of the mean-field structure.