  We investigate, both numerically and analytically, the time evolution of a
particle in an initial plane wave state as it is subject to elastic scattering
in a two-dimensional disordered system with spin-orbit coupling (SOC). In the
analytic calculation, we treat the SOC non-perturbatively, and the disorder
perturbatively using the Diffuson and the Cooperon. We identify weak and strong
SOC regimes, and give the relevant time and energy scales in each case. We
calculate the time dependence of coherent backscattering (CBS) as a function of
the strength of the SOC. By studying the time dependence of the anisotropy of
the disorder-averaged momentum distribution we identify the spin relaxation
time. We find a crossover from D'yakonov-Perel' spin relaxation for weak SOC to
Elliot-Yafet like behaviour for strong SOC.

Quantum Gases;Disordered Systems and Neural Networks;Mesoscale and Nanoscale Physics