  We present a non perturbative and formally exact approach for charge
transport in interacting nanojunctions based on a real time path integral
formulation of the reduced system dynamics. An expansion of the influence
functional in terms of the number of tunneling transitions, and integration of
the Grassmann variables between the tunneling times, allows us to obtain a
still exact generalized master equation (GME) for the populations of the
reduced density matrix (RDM) in the occupation number representation, as well
as a formally exact expression for the current. By borrowing the nomenclature
of the famous spin-boson problem, we characterize the two-state dynamics of
such degrees of freedom on the forward and backward branches in terms of single
four-state paths with alternating blips and sojourns. This allows a
diagrammatic representation of the GME kernel and its parametrization in terms
of sequences of blips and sojourns. We apply our formalism to the exactly
solvable resonant level model (RLM) and to the the single impurity Anderson
model (SIAM), the latter being a prototype system for studying strong
correlations. For both systems, we demonstrate a hierarchical diagrammatic
structure of the exact GME kernel. While the hierarchy closes at the
second-tier level for the RLM, this is not the case for the interacting SIAM.
Upon inspection of the GME, known results from various perturbative and
nonperturbative approximation schemes to quantum transport in the SIAM are
recovered. Finally, a noncrossing approximation for the hierarchical kernel is
developed, which enables us to systematically decrease temperature at each next
level of the approximation. Analytical results for a simplified fourth-tier
scheme are presented.
