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

By applying a sudden perturbation to one of the components mixture two quantum fluids, we explore effect on motion second component short timescale. implementing theory, prove that for times response is fixed by energy weighted moment crossed dynamic structure factor (crossed $f$-sum rule). We also show properly monitoring time duration it possible identify peculiar fast spin drag regimes, which are sensitive interaction effects in Hamiltonian. Special focus given case coherently coupled Bose-Einstein condensates, interacting Bose mixtures exhibiting Andreev-Bashkin effect, normal Fermi liquids, and polaron problem. The relevant excitations system contributing identified contribution low-frequency gapless rule density channels explicitly calculated employing proper macroscopic theories. Both spatially periodic Galilean boost perturbations considered.