Fermi liquid theory applied to a film on an oscillating substrate

TL;DR

This paper extends Fermi liquid theory to analyze how transverse oscillations transmit through a thin Fermi liquid film, considering finite thickness and boundary conditions, with implications for understanding normal-state helium-3 dynamics.

Contribution

It adapts existing Fermi liquid response calculations for infinite layers to finite films with different boundary conditions, incorporating both zero sound and quasiparticle excitations.

Findings

Numerical solutions for finite film oscillation transmission.

Analysis of free surface versus confined boundary effects.

Enhanced understanding of Fermi liquid acoustic impedance.

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.