  We consider the conductivity of excitations in short chains of optical
cavities with two-level atoms in the models of JCH type, where either we
explicitly take into account the photon jumps between atoms, or is merely a
transfer of excitation from atom to atom. We found a non-trivial dependence of
the conductivity on the intensity of runoff and inflow (quantum bottleneck) in
the presence of dephasing noise (the effect of dephasing assisted transport).
