Backflow and density excitations in quantum fluids

Abstract

By the use of the f sum rule and a separation of density excitations into single and multiple excitations, we derive exact quantum expressions for the backflow contribution to the dynamic structure function S(k, Ω) and for the discrete single-excitation spectrum Ω k . The derivation is carried out for Bose liquids, Fermi liquids, charged quantum liquids, quantum solutions, an impurity atom dissolved in quantum fluids, and phonons in solids. It is shown that the backflow arises from virtual multiexcitations and that real multiexcitations give rise to a background. It is argued that multiexcitations are relatively insensitive to long-range order or quantum statistics. Thus the backflow and background contributions to S(k, Ω) of the liquid and solid phases of 4He, and also that to S(k) of liquid 3He and of liquid 4He, are expected to be similar, which is consistent with existing data. The exact expression for Ω k , which shows that multiexcitations effectively repel the single excitations, is used to make some speculations concerning the large-wavevector phonon spectrum in liquid 3He and in 3He-4He solutions.