Theory of domain formation in inhomogeneous ferromagnetic dipolar condensates

Recent experimental studies of $^{87}$Rb spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition taking into account the effects of the trap, non-linearities, finite temperature and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system and estimate the contribution of quantum zero-point fluctuations to the domain formation. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.