Abstract
Analytical properties of dispersion equations in the Landau theory of Fermi liquid and its quantum extension (the linearized time-dependent Hartree-Fock theory) are studied. We find that there does not appear Landau damping solution in the Landau theory with one Landau parameterF0. On the other hand, the quantum theory has complex zeros in dispersion functions for weak repulsive interactions. Calculation of the strength function exhibits a pronounced resonance peak corresponding to Landau damping of the zero sound.
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