2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174520We 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 $j=-κ(τ)\nabla ρ$ where $τ$ is a typical timescale of the lattice fluctuations and $\nabla ρ$ the density gradient imposed %on the system by the reservoirs.Statistical Mechanicstext