Manifold mixing in the temporal evolution of a spin-1 spinor Bose-Einstein condensate

Hydrodynamics of the spin-1 Bose-Einstein condensate is investigated without restriction of its allowed manifold to either the ferromagnetic or the antiferromagnetic phase. Mixing of the two manifolds is found to be a generic feature in the temporal evolution of the condensate, regardless of the sign and strength of the spin-dependent interaction. Hydrodynamic theory is developed based on a new representation of the spin-1 condensate wave function as a linear combination of the well-known wave functions specific to antiferromagnetic and ferromagnetic manifolds only. Dynamical constraints unique to each submanifold are derived for the first time, demonstrating that efforts to write down hydrodynamic theory in one specific manifold are generally invalid. Certain exceptions, such as a uniform spiral state in the antiferromagnetic manifold, are shown to sustain dynamical evolution within the same manifold over time.