  We study fermions that are gauge-coupled to a cavity mode via Raman-assisted
hopping in a one dimensional lattice. For an infinite lattice, we find a
superradiant phase with infinitesimal pumping threshold which induces a
directed particle flow. We explore the fate of this flow in a finite lattice
with boundaries, studying the non-equilibrium dynamics including fluctuation
effects. The short time dynamics is dominated by superradiance, while the long
time behaviour is governed by cavity fluctuations. We show that the steady
state in the finite lattice is not unique, and can be understood in terms of
coherent bosonic excitations above a Fermi surface in real space.
