Quasiparticle relaxation rate and shear viscosity of superfluid 3He-A_1 at low temperatures

TL;DR

This paper calculates the quasiparticle relaxation rate and shear viscosity of superfluid 3He-A_1 at low temperatures, showing their temperature dependence and agreement with experimental data.

Contribution

It provides a detailed theoretical calculation of quasiparticle relaxation and shear viscosity in superfluid 3He-A_1 using Boltzmann equations, considering interactions between quasiparticles.

Findings

Both relaxation rates are proportional to T^2.

Shear viscosities are proportional to (T/T_c)^{-2}.

Results agree with experimental measurements.

Abstract

Quasiparticle relaxation rate,$\tau_{p}^{-1}$, and the shear viscosity tensor of the A_1-phase of superfluid 3He are calculated at low temperatures and melting pressure, by using Boltzmann equation approach in momentum space. The collision integral is written in terms of inscattering and outscattering collision integrals. The interaction between normal and Bogoliubov quasiparticles is considered in calculating transition probabilities in the binary, decay and coalescence processes. We obtain that both $\tau_{p\uparrow}^{-1}$ and $\tau_{p\downarrow}^{-1}$ are proportional to $T^2$ >. The shear viscosities $\eta_{xy}$, $\eta_{xz}$ and $\eta_{zz}$ are proportional to $(T/T_c)^{-2}$. The constant of proportionality of the shear viscosity tensor is in nearly good agreement with the experimental results of Roobol et al., and our exact theoretical calculation.