Out-of-equilibrium bosons on a one-dimensional optical random lattice

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.