  Electrical conductivity of one-dimensional (1d) disordered solids decays
exponentially with their length, which is a celebrated manifestation of the
localization phenomenon. Here, we study the modifications of localized
conductivity induced by placement of 1d semiconductors inside of single-mode
electromagnetic cavities, focusing on the regime of non-degenerate doping. We
use the Green's function technique modified for the non-perturbative account of
cavity excited states, and including both coherent electron-cavity effects
(i.e. electron motion in the zero-point fluctuating field) and incoherent
processes of photon emission upon tunneling. The energy spectrum of electron
transmission in the cavity acquires Fano-type resonances associated with
virtual photon emission, passage along the resonant level, and photon
re-absorption. The quality factor of the Fano resonance depends on whether the
intermediate state is coupled to the leads, and reaches its maximum when this
state is localized deep in the disorder potential. Coupling to the cavity also
elevates the energies of the shallow bound states, bringing them to the
conduction band bottom. Such an effect leads to the enhancement of the
low-temperature conductance.
