Fermi liquid theory applied to vibrating wire measurements in 3He-4He mixtures

TL;DR

This paper applies Fermi liquid theory to analyze the mechanical impedance of 3He-4He mixtures in vibrating wire experiments, providing numerical results that align well with experimental observations across different quasiparticle mean-free-path regimes.

Contribution

It introduces a comprehensive numerical approach solving the Landau-Boltzmann equation for 3He quasiparticles, incorporating the two-fluid nature and boundary effects in vibrating wire measurements.

Findings

Reproduces the decrease in inertia at the ballistic limit.

Demonstrates the influence of container and second-sound resonances.

Achieves fair quantitative agreement with experimental data.

Abstract

We use Fermi liquid theory to study the mechanical impedance of 3He-4He mixtures at low temperatures. The theory is applied to the case of vibrating wires, immersed in the liquid. We present numerical results based on a direct solution of Landau-Boltzmann equation for the 3He quasiparticle distribution for the full scale of the quasiparticle mean-free-path. The two-fluid nature of mixtures is taken into account in the theory, and the effect of Fermi liquid interactions and boundary conditions are studied in detail. The results are in fair quantitative agreement with experimental data. In particular, we can reproduce the anomalous decrease in inertia, observed in vibrating wire experiments reaching the ballistic limit. The essential effect of the experimental container and second-sound resonances is demonstrated.