  We devise a semi-classical model to describe the transport properties of
low-dimensional fermionic lattices under the influence of external quantum
stochastic noise. These systems behave as quantum stochastic resistors, where
the bulk particle transport is diffusive and obeys the Ohm/Fick's law. Here, we
extend previous exact studies beyond the one-dimensional limit to ladder
geometries and explore different dephasing mechanisms that are relevant to
different physical systems, from solid-state to cold atoms. We find a
non-trivial dependence of the conductance of these systems on the chemical
potential of the reservoirs. We then introduce a semi-classical approach that
is in good agreement with the exact numerical solution and provides an
intuitive and simpler interpretation of transport in quantum stochastic
resistors. Moreover, we find that the conductance of quantum ladders is
insensitive to the coherence of the dephasing process along the direction
transverse to transport, despite the fact that the system reaches different
stationary states. We conclude by discussing the case of dissipative leads
affected by dephasing, deriving the conditions for which they effectively
behave as Markovian injectors of particles in the system.
