  Spin-orbit interactions in two-dimensional electron liquids are responsible
for many interesting transport phenomena in which particle currents are
converted to spin polarizations and spin currents and viceversa. Prime examples
are the spin Hall effect, the Edelstein effect, and their inverses. By similar
mechanisms it is also possible to partially convert an optically induced
electron-hole density wave to a spin density wave and viceversa. In this paper
we present a unified theoretical treatment of these effects based on quantum
kinetic equations that include not only the intrinsic spin-orbit coupling from
the band structure of the host material, but also the spin-orbit coupling due
to an external electric field and a random impurity potential. The
drift-diffusion equations we derive in the diffusive regime are applicable to a
broad variety of experimental situations, both homogeneous and non-homogeneous,
and include on equal footing "skew scattering" and "side-jump" from
electron-impurity collisions. As a demonstration of the strength and usefulness
of the theory we apply it to the study of several effects of current
experimental interest: the inverse Edelstein effect, the spin-current swapping
effect, and the partial conversion of an electron-hole density wave to a spin
density wave in a two-dimensional electron gas with Rashba and Dresselhaus
spin-orbit couplings, subject to an electric field.
