Acoustic impedance of a Fermi liquid film

Landau’s Fermi liquid theory is a seminal work in the field of many-body theories. It employs the concept of quasiparticles to describe the dynamics of a mass of interacting fermions, in this case liquid helium-3. Quasiparticles are particle-like excitations of the entire fermion system that behave in a much simpler manner than the actual particles. Fermi liquid theory predicts the existence of new collective excitation modes called zero sound. These are sound-like oscillations that exist even in the absence of particle collisions and their presence can be probed by measuring the acoustic impedance of the liquid. Acoustic impedance indicates how a fluid responds to excitations. The purpose of this Master’s thesis is to calculate the transverse or shear acoustic impedance of a film of helium-3 as the film is being excited by an oscillating planar surface. This is done by developing the linearized Landau transport equation into a form that is amendable to a solution. An expression for the transverse acoustic impedance of a helium-3 film is then derived. The acoustic impedance is calculated using numerical methods. This includes discretizing a group of integral equations and using linear algebra to solve them. Along with the numerical model itself, some results of these calculations are then presented and analyzed. The numerical model behaves well for a wide range of parameter values and the results of the model conform to two analytically solvable limiting cases. The main focus of this work has been on developing the numerical model itself and the results have yet to be compared to experimental data