Effects of phase fluctuation on a mixture of rotating superfluids

It is shown that if the root-mean-square of the gradient of the phase fluctuation of either of the components exceeds the corresponding inverse of the coherence length or if the chemical potential exceeds ₁⁰ or ₂⁰, where is the volume integrals of the interaction function between the components, and ₁⁰, ₂⁰ are the densities of the two components, the mixture of two rotating superfluids has an instability.