Spin dynamics in a polarized Bose gas.

Abstract

The equation of motion for the spin density of a spin-polarized Bose gas is derived for low temperatures down to ${\mathit{T}}_{\mathit{c}+}$, the critical temperature of Bose-Einstein condensation. In the classical regime, our results agree with those of Lhuillier and Lalo\"e. However, at low T, ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\parallel}}}$ become qualitatively different, especially at larger polarization M, and are no longer proportional to ${\mathit{T}}^{\mathrm{\ensuremath{-}}1/2}$. Particularly, ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ reaches a maximum at T\ensuremath{\sim}1.6${\mathit{T}}_{\mathit{c}+}$ and decreases thereafter so that intrinsic spin-wave damping in a Bose gas increases with decreasing T for T1.6${\mathit{T}}_{\mathit{c}+}$.