Fourier's law on a one-dimensional optical random lattice

We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate 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 $j=-κ(τ)\nabla n$ where $τ$ is a typical timescale of the lattice fluctuations and $\nabla n$ the density gradient imposed by the reservoirs.

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