Fermi liquid theory applied to a film on an oscillating substrate

Abstract

We have studied the transmission of transverse oscillations through a thin Fermi liquid film, using Landau's Fermi liquid theory. Fermi liquid theory describes the dynamics of interacting, degenerate fermion systems, for example non-superfluid, i.e.\ normal state \textsuperscript{3}He at millikelvin temperatures. The response of a Fermi liquid to the transverse oscillations of a planar substrate has previously been calculated for a fluid layer of infinite thickness. We have modified these calculations for application to a film of finite thickness, either with a free surface, or as confined between two parallel substrates. The equations take into account contributions to the acoustic impedance from both the collective transverse zero sound mode, as well as the incoherent single-quasiparticle excitations and are solved using numerical methods.Comment: 11 pages, 8 figures. Updated to published version. Changes in presentation, no change in result

Two-parameter boundary condition applied to transverse acoustic impedance of a Fermi liquid

“…The shown results complement the special cases studied in Ref. [12]. Other parameters are q = 0.75, Ω = 1, and F 2 = 0.…”

“…forp ·n > 0. For transverse impedance with u = ux, the distribution takes the form ψp = cos φ sin θ ψ(cos θ, ζ), where ζ is the dimensionless vertical coordinate in the liquid [12]. The BRDF (8) then leads to the boundary condition…”

“…Figure 1. The acoustic impedance Z of a Fermi liquid film with a free upper surface: the real and imaginary parts as a parametric plot with parameter l/d [12]. The red/black curves are labelled by the momentum transfer efficiency q = 0.5, 0.1, 0.05 and 0.01.…”

“…As all quasiparticles effectively propagate at the Fermi velocity v F , we can apply the general boundary condition (1) directly to the quasiparticle distribution function. We use the energy-integrated distribution ψ p, which gives the local energy shift of the Fermi surface relative to the equilibrium Fermi level [5,12]. Taking into account that the surface is moving with velocity u, we have to replace ψ p → ψ p − p F p • u [5].…”

“…We formulate a general boundary using BRDF and propose a simple generalization of the diffusespecular boundary condition that has a tilt in the diffusive part. We apply the boundary condition to a normal-state Fermi liquid film on a transversely oscillation plane [12]. Besides presenting results of the new boundary condition, some additional results are shown.…”