Hydrodynamic Stability ofHe3-A

Abstract

The stability of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ with uniform superflow is examined in the hydrodynamic limit. Below the threshold found by Bhattacharyya, Ho, and Mermin, any reasonable choice of hydrodynamic parameters renders the uniform texture stable with respect to general three-dimensional perturbations. Beyond threshold, the texture undergoes a transition to a static helix, whose broken translational symmetry complicates the general stability analysis. In a truncated variational approximation, this structure is stable near threshold with respect to perturbations proportional to $\exp \left(i\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{r}}\right)$.