  We review the structure of the conservation laws in noninteracting spin
chains and unveil a formal expression for the corresponding currents. We
briefly discuss how interactions affect the picture. In the second part, we
explore the effects of a localized defect. We show that the emergence of
spontaneous currents near the defect undermines any description of the
late-time dynamics by means of a stationary state in a finite chain. In
particular, the diagonal ensemble does not work. Finally, we provide numerical
evidence that simple generic localized defects are not sufficient to induce
thermalization.
