Quantum Spin Dynamics of Spin-1 Bose Gas

We show that the quantum evolution of a spin-1 Bose gas with nearly all bosons initially in the $F_z = 0$ state has a "quantum carpet" {\em spin-time} structure with self-similar properties. The system continuously evolves into "multi-peaked" Schr\"odinger cat like states, returning occasionally to coherent structures, which leads to large number fluctuations (as seen in recent experiments). The self similar behavior allows one to reveal the quantum evolution as a set of peaks in the number probability distribution of a spin component at times {\em much shorter} than the quantum revival time. We also show that these features survive small number fluctuations among spin components up to a few percent.