  Quantum drift-diffusion equations are derived for a two-dimensional electron
gas with spin-orbit interaction of Rashba type. The (formal) derivation turns
out to be a non-standard application of the usual mathematical tools, such as
Wigner transform, Moyal product expansion and Chapman-Enskog expansion. The
main peculiarity consists in the fact that a non-vanishing current is already
carried by the leading-order term in the Chapman-Enskog expansion. To our
knowledge, this is the first example of quantum drift-diffusion equations
involving the full spin vector. Indeed, previous models were either quantum
bipolar (involving only the spin projection on a given axis) or full spin but
semiclassical.
