Population Dynamics of a Spin-1 Bose Gas at Finite Temperatures

We study population dynamics of a trapped spin-1 Bose gas above the Bose-Einstein transition temperature. Starting from the semiclassical kinetic equation for a spin-1 gas, we derive coupled rate equations for the populations of internal states. Solving the rate equations, we study the dynamical evolution of spin populations. We also estimate the characteristic timescale in which the system reaches equilibrium. Finally, we briefly discuss the extension of the theory to Bose-condensed phase below the Bose-Einstein transition temperature, and discuss the static equilibrium condition for the spin-1 system.