  We study interacting one dimensional (1D) quantum lattice gases with
integrable impurities. These model Hamiltonians can be derived using the
quantum inverse scattering method for inhomogeneous models and are by
construction integrable. Absence of backscattering at the impurities is shown
to be the characteristic feature of these disordered systems. The value of the
effective carrier charge and the Sutherland-Shastry relation are derived for
the half-filled XXX model and are shown to be independent of the impurity
concentration and strength. For the half-filled XXZ model we show that there is
no enhancement of the persistent currents for repulsive interactions. For
attractive interactions we identify a crossover regime beyond which enhancement
of the currents is observed.
