We study the breaking of global discrete symmetries -specifically inversion and translation- in one-dimensional scattering set-ups. We focus on the case where the broken global symmetry is retained locally, in arbitrary domains of finite spatial extent and we find a class of space invariant, non-local currents, which are remnants of the broken global symmetry. The proposed method addresses successfully any combination of translation and inversion symmetry and can be applied to the study of wave propagation in aperiodic and quasi-periodic media.
