Twisting in superfluidA3and consequences for hydrodynamics atT=0

We study the effects of twisting on the low-energy excitations of superfluid ${}_{}{}^3{}_{}{}^{}\mathit{A}$. They are small compared to the effects of bending, but they have a different symmetry which makes them important. The structure of the excitation wave functions has strong analogies with the eigenstates of a charged particle in a magnetic field. The group velocity is parallel to curl l^. The density of states at zero energy has a contribution proportional to twisting which is odd with respect to k^. Because of this term a density fluctuation produces a fluctuation of the current carried by the excitations. This current fluctuation turns out to be exactly equal to the fluctuation of the $C_0$ term in the current. This shows that the $C_0$ term fluctuation is carried by the normal liquid and leads us to believe that the $C_0$ term as a whole is linked to the normal liquid. Since calculations making use of the Bardeen-Cooper-Schrieffer wave function consider only the condensate, our results offer a possible explanation for the ‘‘angular-momentum paradox.’’ We physically interpret the ${\mathrm{v}}_n$ term in the Josephson equation at T=0 and show that it is readily obtained from the microscopic description of the normal liquid. In the same way we deduce from the momentum conservation law an equation of motion for ${\mathrm{v}}_n$ and we show that it can be entirely understood from the microscopic framework.