  A model consisting in two quantum XX spin chains, one homogeneous and the
second with random couplings drawn from a binary distribution, is considered.
The two chains are coupled to two different non-local thermal baths and their
dynamics is governed by a Lindblad equation. In the steady state, a current J
is induced between the two chains by coupling them together by their edges and
imposing different chemical potentials $\mu$ to the two baths. While a regime
of linear characteristics J versus $\Delta$$\mu$ is observed in the absence of
randomness, a gap opens as the disorder strength is increased. In the
infinite-randomness limit, this behavior is related to the density of states of
the localized states contributing to the current. The conductance is shown to
diverge in this limit.
