Transverse relaxation in two-level Fermi liquids and gases

Abstract

An exact microscopic theory is developed for transverse dynamics in two-level Fermi systems like spin-polarized Fermi liquids. The origin of a transverse zero-temperature attenuation is a dephasing of interlevel transitions in inhomogeneous conditions. We analyze different sources of this relaxation using an extrapolation from low polarizations or densities. These sources include imaginary terms in the vertex and single-particles' energies and pseudo-energies away from the Fermi spheres, and derivatives of the vertex function in off-shell directions. The attenuation for dilute systems starts from a second order term in density. The main non-local contribution is of the next order in density, but is not negligible if the interaction range is large. At very low polarizations and densities, one recovers the already known results. The implications for liquid³He↑ and³He↑-⁴He mixtures are discussed.