  We study the transport properties of a one-dimensional hard-core boson
lattice gas coupled to two particle reservoirs at different chemical potentials
generating a current flow through the system. In particular, the influence of
random fluctuations of the underlying lattice on the stationary state
properties is investigated. We show analytically that the steady-state density
presents a linear profile. The local steady-state current obeys the Fourier law
$j=-\kappa(\tau)\nabla \rho $ where $\tau$ is a typical timescale of the
lattice fluctuations and $\nabla \rho$ the density gradient imposed %on the
system by the reservoirs.
