Nonadiabatic quantum phase transition in a trapped spinor condensate

We study the effect of an external harmonic trapping potential on an outcome of the nonadiabatic quantum phase transition from an antiferromagnetic to a phase-separated state in a spin-1 atomic condensate. Previously, we demonstrated that the dynamics of an untrapped system exhibits double universality with two different scaling laws appearing due to the conservation of magnetization. We show that in the presence of a trap, double universality persists. However, the corresponding scaling exponents are strongly modified by the transfer of local magnetization across the system. The values of these exponents cannot be explained by the effect of causality alone, as in the spinless case. We derive the appropriate scaling laws based on a slow diffusive-drift relaxation process in the local density approximation.