  Here, the particle-wave duality principle is generalized to accommodate the
non-relativistic quantum mechanics of interacting (correlated) particles.
Through the creation and propagation of concurrent stochastic ensembles of
walkers in physical and in Hilbert spaces one can correctly predict the ground
state and the time evolution of a subsystem of a larger quantum system in a
quantum Monte Carlo manner. It is shown that such walker ensembles can be
constructed straightforwardly through a random sampling (windowing) applied to
the mean-field approximation. Our calculations reveal that although the
resulting individual quantum trajectories may differ significantly from those
predicted by the many-body Schr\"odinger equation, the evolution of the
particle distribution and the decoherence due to the Coulomb interaction can be
accounted for correctly using an explicitly parameterized quantum non-locality.
