Hydrodynamics ofHe3−Bin high magnetic fields

Abstract

We derive the hydrodynamic equations for $^{3}\mathrm{He}\ensuremath{-}B$ in high magnetic fields. The order parameter is a nonunitary spin-orbit matrix and the orbit space is uniaxial. The influence of a strong magnetic field shows up in various features. There exists a third velocity which transforms only partially like a velocity under Galilean transformation. Many coupling terms between spin space and orbit space are found in the static as well as in the reversible and dissipative dynamical equations. The resulting main features are the mixing of first and second (and fourth) sound with longitudinal spin waves and the anisotropy of the material parameters. The value of the rotation angle ${\ensuremath{\theta}}_{0}$, which minimizes the magnetic dipole energy, is lowered, the longitudinal NMR frequency is raised, and the transverse NMR frequency is shifted in $^{3}\mathrm{He}$-$^{3}\mathrm{He}\ensuremath{-}B$ in high magnetic fields.