  We perform a study of the effect of the high in-plane electric field on the
spin precession and spin dephasing due to the D'yakonov-Perel' mechanism in
$n$-type GaAs (100) quantum wells by constructing and numerically solving the
kinetic Bloch equations. We self-consistently include all of the scattering
such as electron-phonon, electron-non-magnetic impurity as well as the
electron-electron Coulomb scattering in our theory and systematically
investigate how the spin precession and spin dephasing are affected by the high
electric field under various conditions. The hot-electron distribution
functions and the spin correlations are calculated rigorously in our theory. It
is found that the D'yakonov-Perel' term in the electric field provides a
non-vanishing effective magnetic field that alters the spin precession period.
Moreover, spin dephasing is markedly affected by the electric field. The
important contribution of the electron-electron scattering to the spin
dephasing is also discussed.
