Geometric phase for open quantum systems and stochastic unravellings
  We analyze the geometric phase for an open quantum system when computed by resorting to a stochastic unravelling of the reduced density matrix (quantum jump approach or stochastic Schrodienger equations). We show that the resulting phase strongly depends on the type of unravelling used for the calculations: as such, this phase is 'not' a geometric object since it depends on non-physical parameters which are not related to the path followed by the density matrix during the evolution of the system. 
A. Bassi, E. Ippoliti