Strong spin-oscillation of small spin-1 condensates caused by an inclined weak magnetic field

When a magnetic field is applied along a direction deviated from the quantization $Z$-axis, the conservation of total magnetization holds no more. In this case the inclined field can cause a strong spin-evolution via the linear Zeeman term even the field is as weak as a percentage of $mG$. An approach beyond the mean field theory is proposed to study the evolution of small ${}^{87}$Rb condensates under the weak inclined fields. The time-dependent populations of spin-components are given in analytical forms. The evolution is found to be highly sensitive to the magnitude and direction of the field.