  We study the interplay between charge transport and light-matter interactions
in a confined geometry, by considering an open, mesoscopic chain of two-orbital
systems resonantly coupled to a single bosonic mode close to its vacuum state.
We introduce and benchmark different methods based on self-consistent solutions
of non-equilibrium Green's functions and numerical simulations of the quantum
master equation, and derive both analytical and numerical results. It is shown
that in the dissipative regime where the cavity photon decay rate is the
largest parameter, the light-matter coupling is responsible for a steady-state
current enhancement scaling with the cooperativity parameter. We further
identify different regimes of interest depending on the ratio between the
cavity decay rate and the electronic bandwidth. Considering the situation where
the lower band has a vanishing bandwidth, we show that for a high-finesse
cavity, the properties of the resonant Bloch state in the upper band are
transfered to the lower one, giving rise to a delocalized state along the
chain. Conversely, in the dissipative regime with low cavity quality factors,
we find that the current enhancement is due to a collective decay of
populations from the upper to the lower band.
