| Popis: |
In this paper, we develop an appropriate set of hydrodynamic equations for a U(N) invariant superfluid that couple the dynamics of superflow and magnetization. In the special case when both the superfluid and normal velocities are zero, the hydrodynamic equations reduce to a generalized version of Landau–Lifshitz equation for ferromagnetism with U(N) symmetry. When both velocities are non-zero, there appears couplings between the superflow and magnetization dynamics, and the superfluid velocity no longer satisfies the irrotational condition. On the other hand, the magnitude of magnetization is no longer a constant of motion as was the case for the standard Landau–Lifshitz theory. In comparison with the simple superfluid, the first and second sounds are modified by a non-zero magnetization through various thermodynamic functions. For U(2) invariant superfluid, we get both (zero-) sound wave and a spin wave at zero temperature. It is found that the dispersion of spin wave is always quadratic, which is consistent with microscopic analysis. In the appendix , we show that the hydrodynamic equation for a U(N) invariant superfluid can be obtained from the general hydrodynamic equation with arbitrary internal symmetries. |
