  We discuss the dynamics of an open two-mode Bose-Hubbard system subject to
phase noise and particle dissipation. Starting from the full many-body dynamics
described by a master equation the mean-field limit is derived resulting in an
effective non-hermitian (discrete) Gross-Pitaevskii equation which has been
introduced only phenomenologically up to now. The familiar mean-field phase
space structure is substantially altered by the dissipation. Especially the
character of the fixed points shows an abrupt transition from elliptic or
hyperbolic to attractiv or repulsive, respectively. This reflects the
metastable behaviour of the corresponding many-body system which surprisingly
also leads to a significant increase of the purity of the condensate. A
comparison of the mean-field approximation to simulations of the full master
equation using the Monte Carlo wave function method shows an excellent
agreement for wide parameter ranges.
