Hydrodynamics ofHe3-Awith Arbitrary Textures

Abstract

The general condition that determines the equilibrium textures of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ incorporating the interdependence of ${\overrightarrow{\mathrm{V}}}^{\mathrm{}\left(s\right)\mathrm{}}$, $l_i$, and ${\partial }_i{l}_j$, is derived. This condition is used to generalize Graham's hydrodynamics to allow for arbitrary equilibrium textures and steady-state flow. A new procedure is introduced to ensure that angular momentum is locally conserved; it is found to imply various relations between certain reaction coefficients.