Department of Physics2024-11-0920032469-992610.1103/PhysRevA.68.0136132-s2.0-85037245557https://hdl.handle.net/20.500.14288/3663We discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground-state distribution of the phases associated with the total atom number (N), the total magnetization (M), and the alignment (or hypercharge) (Y) of the system. The mean-field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recovering the two broken continuous symmetries [U(1) and SO(2)] when N and M are conserved, as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with antiferromagnetic interactions.pdfOpticsPhysicsJournal Article1094-1622https://doi.org/10.1103/PhysRevA.68.013613184571600112Q1NOIR00730