  The transport properties of a conduction junction model characterized by two
mutually coupled channels that strongly differ in their couplings to the leads
are investigated. Models of this type describe molecular redox junctions (where
a level that is weakly coupled to the leads controls the molecular charge,
while a strongly coupled one dominates the molecular conduction), and electron
counting devices in which the current in a point contact is sensitive to the
charging state of a nearby quantum dot. Here we consider the case where
transport in the strongly coupled channel has to be described quantum
mechanically (covering the full range between sequential tunneling and
co-tunneling), while conduction through the weakly coupled channel is a
sequential process that could by itself be described by a simple master
equation. We compare the result of a full quantum calculation based on the
pseudoparticle non-equilibrium Green function method to that obtained from an
approximate mixed quantum-classical calculation, where correlations between the
channels are taken into account through either the averaged rates or the
averaged energy. We find, for the steady state current, that the approximation
based on the averaged rates works well in most of the voltage regime, with
marked deviations from the full quantum results only at the threshold for
charging the weekly coupled level. These deviations are important for accurate
description of the negative differential conduction behavior that often
characterizes redox molecular junctions in the neighborhood of this threshold.
