Phase diffusion of a two-component Bose-Einstein condensates:exact and short-time solutions for arbitrary coherent spin state

We investigate phase diffusion of a two-component Bose--Einstein condensates prepared initially in arbitrary coherent spin state |\theta_0,\phi_0\rangle. Analytical expression of the phase-diffusion time is presented for \theta_0\neq\pi/2 case. In comparison with the symmetrical case (i.e., \theta_0=\pi/2), we find that the diffusion process becomes slow due to the reduced atom number variance.