Viscoelastic behavior in a normal Fermi liquid

Abstract

Effective elastic coefficients for a normal Fermi liquid at finite frequency ω and wave vectorq are calculated microscopically from the Landau kinetic equation. We find in general that there are three elastic moduli in a normal Fermi liquid. One is just the usual bulk modulus and the other two are associated with the transverse and longitudinal shears of the liquid. This is in contrast to the viscoelastic model, in which a single modulus characterizes both transverse and longitudinal shear. The shear moduli that we have calculated are functions of ω/qv _F, wherev _F is the Fermi velocity, and they become equal only when ω/q is much larger thanv _F. In this limit we show that a viscoelastic model provides a reasonable quantitative description of the propagation and attenuation of the collective modes of a normal Fermi liquid. We also consider the applicability of the viscoelastic model to³He and find that it provides a reasonable first approximation to longitudinal sound and only a crude first approximation to transverse sound.