  Multi-component quantum mixtures in one dimension can be characterized by
their symmetry under particle exchange. For a strongly-interacting Bose-Bose
mixture, we show that the time evolution of the momentum distribution from an
initially symmetry-mixed state is quasi-constant for a SU(2) symmetry
conserving Hamiltonian, while it displays large oscillations in time for the
symmetry-breaking case where inter- and intra-species interactions are
different. Using the property that the momentum distribution operator at strong
interactions commutes with the class-sum operator, the latter acting as a
symmetry witness, we show that the momentum distribution oscillations
correspond to symmetry oscillations, with a mechanism analog to neutrino
flavour oscillations.
