The dynamic Hartree-Fock theory with point-like interaction is used to calculate the speed of sound and damping factor of a zero-sound wave propagating in a degenerate Fermi gas. This wave propagates slower than Fermi velocity. It is shown, that if the interaction is weak and density is small, then the damping of such a wave can be small. A possibility of discovering such waves in ultracold Fermi gases is discussed.
We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the effective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.
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