  We investigate the second-order von Neumann approach from a diagrammatic
point-of-view and demonstrate its equivalence with the resonant tunneling
approximation. Investigation of higher-order diagrams shows that the method
correctly reproduces the equation of motion for the single-particle reduced
density matrix of an arbitrary non-interacting many-body system. This explains
why the method reproduces the current exactly for such systems. We go on to
show, however, that diagrams not included in the method are needed to calculate
exactly higher cumulants of the charge transport. This thorough comparison
sheds light on the validity of all these self consistent second-order
approaches. We analyze the discrepancy between the noise calculated by our
method and the exact Levitov formula for a simple non-interacting quantum dot
model. Furthermore we study the noise of the canyon of current suppression in a
two-level dot, a phenomenon that requires the inclusion of electron-electron
interaction as well as higher-order tunneling processes.
