Transverse Dynamics in Spin-Polarized and Binary Fermi Liquids.

I discuss transverse dynamics in spin-polarized Fermi liquids such as itinerant magnets, ^3 Heuparrow, and ^3 Heuparrow-^4 He mixtures. I derive exact microscopic equations of transverse dynamics in spin-polarized and binary Fermi liquids at zero temperature using the Green's functions method. The transverse dynamics is described by an inherently nonlocal integral equation in a 4D momentum space. This equation is equivalent to a set of two coupled equations for "partial transverse densities" which correspond generically to contributions from tilted spin-ups and spin-downs. In contrast to previous phenomenological attempts to describe polarized Fermi liquids, these two equations reduce to a single Landau-like kinetic equation only for low polarization or density. The molecular field has the form of a 4-component complex nonlocal operator. This interaction operator is related to the exact irreducible vertex via an integral equation, and cannot be given, as it is usually assumed, as any limit of the full vertex. The dephasing of inhomogeneous precession of dressed spin-up and spin-down pseudoparticles leads to a peculiar zero-temperature attenuation. The case of a dilute Fermi gas is analyzed by means of perturbation theory. I demonstrate how the exact theory reduces to the conventional theory of highly polarized dilute Fermi gases. For an ideal polarized Fermi gas and in the first order in density, the theory assumes the standard form. In the next order, the main equations still have a fairly conventional form, though they already contain the peculiar zero-temperature attenuation which is missing in the standard theory. In the third order, the standard theory fails completely, and even the form of equations of transverse dynamics becomes unconventional. The parameters of transverse spin dynamics and the spectrum of spin waves, including zero-temperature attenuation are calculated explicitly. As a by-product, the polarization dependences of the thermodynamic parameters are determined. An application of the results to ^3Heuparrow -^4He mixtures includes effects of non-locality in the direct interaction channel and the retardation in the phonon-mediated part of particle interaction. I also developed a field/polarization expansion for spin dynamics in arbitrary dense Fermi liquids.