  The nonequilibrium dynamics of correlated charge transfer along a
one-dimensional chain in presence of a phonon environment is investigated
within a dissipative Hubbard model. For this generalization of the ubiquitous
spin-boson model the crucial role of symmetries is analysed in detail and
corresponding invariant subspaces are identified. It is shown that the time
evolution typically occurs in each of the disjunct subspaces independently
leading e.g. asymptotically to a non-Boltzmann equilibrium state. Based on
these findings explicit results are obtained for two interacting electrons by
means of a substantially improved real-time quantum Monte Carlo approach. In
the incoherent regime an appropriate mapping of the many-body dynamics onto an
isomorphic single particle motion allows for an approximate description of the
numerical data in terms of rate equations. These results may lead to new
control schemes of charge transport in tailored quantum systems as e.g.
molecular chains or quantum dot arrays.
