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By applying a sudden perturbation to one of the components of a mixture oftwo quantum fluids, we explore the effect on the motion of the second componenton a short time scale. By implementing perturbation theory, we prove that forshort times the response of the second component is fixed by the energyweighted moment of the crossed dynamic structure factor (crossed f-sum rule).We also show that by properly monitoring the time duration of the perturbationit is possible to identify peculiar fast spin drag regimes, which are sensitiveto the interaction effects in the Hamiltonian. Special focus is given to thecase of coherently coupled Bose-Einstein condensates, interacting Bose mixturesexhibiting the Andreev-Bashkin effect, normal Fermi liquids and the polaronproblem. The relevant excitations of the system contributing to the spin drageffect are identified and the contribution of the low frequency gaplessexcitations to the f-sum rule in the density and spin channels is explicitlycalculated employing the proper macroscopic dynamic theories. Both spatiallyperiodic and Galilean boost perturbations are considered.

Spin drag and fast response in a quantum mixture of atomic gases