  We perform a theoretical investigation on the time evolution of spin pulses in an $n$-type GaAs (001) quantum well with and without external electric field at high temperatures by constructing and numerically solving the kinetic spin Bloch equations and the Poisson equation, with the electron-phonon, electron-impurity and electron-electron Coulomb scattering explicitly included. The effect of the Coulomb scattering, especially the effect of the Coulomb drag on the spin diffusion/transport is investigated and it is shown that the spin oscillations and spin polarization reverse along the direction of spin diffusion in the absence of the applied magnetic field, which were originally predicted in the absence of the Coulomb scattering by Weng and Wu [J. Appl. Phys. {\bf 93}, 410 (2003)], can sustain the Coulomb scattering at high temperatures ($\sim 200$ K). The results obtained are consistent with a recent experiment in bulk GaAs but at a very low temperature (4 K) by Crooker and Smith [Phys. Rev. Lett. {\bf 94}, 236601 (2005)]. 
Diffusion and transport of spin pulses in an $n$-type semiconductor   quantum well