Equilibrium order parameters and chemical potentials in rotating superfluids

Elementary microscopic arguments are given showing that in equilibrium the order parameter of a superfluid rotates with the container. We show that this rotating equilibrium is also a consequence of the phenomenological equations of superfluid hydrodynamics, provided considerable care is taken in specifying which variable in those equations is to be identified with the chemical potential. Our results clarify the physics underlying the so-called gauge wheel effects in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, demonstrate that recently raised doubts on the validity of the proposed hydrodynamics of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are misconceived, and make some novel points about the behavior of the superfluid chemical potential under Galilean transformations and its role in the equations of Landau's two-fluid model.