Domain Wall Dynamics in the Spinor Bose-Einstein Condensates

A dynamical theory is presented for the domain wall in the spinor Bose-Einstein condensate of "effective"one-dimension. The formulation is based on the time-dependent Landau-Ginzburg (LG) theory written in terms of the spinor order parameter. The procedure is carried out in such a way that an adiabatic change of the collective coordinates; the kink position as well as the phase function built in the spinor, is adapted to the canonical term (alias geometric phase) in the LG Lagrangian. Two problems are discussed: The first one is to explore the translational motion of the kink center in the presence of the pinning potential, which results in the quantum potential problem. The other one concerns the "steering" of the domain wall by modulating the externally driven magnetic field assisted with dissipation. The present attempt would shed light on the spinor Bose- Einstein condensates from a novel viewpoint.