Competing solutions of Landau's kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

摘要

We examine in detail the method introduced by Sanchez-Castro, Bedell, andWiegers (SBW) to solve Landau's linearized kinetic equation, and compare itwith the well-known standard method introduced by Abrikosov and Khalatnikov(AK). The SBW approach, hardly known, differs from AK in the way that momentsare taken with respect to the angular functions of the Fourier transformedkinetic equation. We compare the SBW and AK solutions for zero-sound andfirst-sound propagation speeds and attenuation both analytically in the zeroand full polarization limits, and numerically at arbitrary polarization usingLandau parameters appropriate for thin $^{3}$He films. We find that the lesserknown method not only yields results in close agreement with the standardmethod, but in most cases does so with far less analytic and computational