Low-energy dynamics of spinor condensates

Austen Lamacraft 2010. Physical Review B


We present a derivation of the low-energy Lagrangian governing the dynamics of the spin degrees of freedom in a spinor Bose condensate for any phase in which the average magnetization vanishes. This includes all phases found within mean-field treatments except for the ferromagnet for which the low-energy dynamics has been discussed previously. The Lagrangian takes the form of a sigma model for the rotation matrix describing the local orientation of the spin state of the gas.