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[en] Quasilinear theory of a weakly turbulent quantum Fermi liquid is presented. Landau linear theory of Fermi liquids is generalized by consideration of weak nonlinear regime. A newly derived kinetic equation of the Fermi particles is used to derive a slowly varying distribution function f0, which satisfies the diffusion equation. It is shown that the magnitude of the diffusion coefficient D depends on weak interactions between atoms and the de Broglie waves diffraction.