  The theory of spin drift and diffusion in two-dimensional electron gases is
developed in terms of a random walk model incorporating Rashba, linear and
cubic Dresselhaus, and intersubband spin-orbit couplings. The additional
subband degree of freedom introduces new characteristics to the persistent spin
helix (PSH) dynamics. As has been described before, for negligible intersubband
scattering rates, the sum of the magnetization of independent subbands leads to
a checkerboard pattern of crossed PSHs with long spin lifetime. For strong
intersubband scattering we model the fast subband dynamics as a new random
variable, yielding a dynamics set by averaged spin-orbit couplings of both
subbands. In this case the crossed PSH becomes isotropic, rendering circular
(Bessel) patterns with short spin lifetime. Additionally, a finite drift
velocity breaks the symmetry between parallel and transverse directions,
distorting and dragging the patterns. We find that the maximum spin lifetime
shifts away from the PSH regime with increasing drift velocity. We present
approximate analytical solutions for these cases and define their domain of
validity. Effects of magnetic fields and initial package broadening are also
discussed.
