Zero-temperature attenuation and transverse spin dynamics in Fermi liquids. I. Generalized Landau theory

Abstract

This is the first in a series of papers on a consistent microscopic theory of transverse dynamics in spin-polarized or binary Fermi liquids. We start from exact microscopic equations in Green's functions at zero temperatures and consider slightly inhomogeneous perturbations. The transverse dynamics is described by an integral equation in a 4D momentum space with inevitable spatial and temporal non-localities. This equation can be reduced only to a set of two coupled equations for partial transverse densities corresponding to independent contributions to a transverse magnetic moment from transverse components of slightly tilted up and down spins. It is shown that, in contrast to previous phenomenological theories of polarized Fermi liquids, these equations reduce to a single Landau-like kinetic equation only in cases of low polarization or density. This implies the existence of two different sorts of (attenuating) transverse quasi-particles. The molecular field (an analog of a Landau function) has a form of a 4-component non-local operator. This interaction operator is expressed via the off-diagonal component of the exact irreducible vertex with the help of some integral equation, and cannot be given, as it is usually assumed, as any limit of the full vertex. The proper Landau-like phenomenological approach corresponding to our exact microscopic equations, should operate with two types of attenuating transverse quasi-particles each oscillating between its Fermi surface and some other 3D surface in a 4D momentum space. The dephasing of inhomogeneous precession between two different types of dressed transverse quasi-particles leads to an inhomogeneous broadening which manifests itself as a peculiar zero-temperature relaxation.