  We study the semi-classical motion of holes by exact numerical solution of
the Luttinger model. The trajectories obtained for the heavy and light holes
agree well with the higher order corrections to the abelian and the non-abelian
adiabatic theories in Ref. [1] [S. Murakami et al., Science 301, 1378(2003)],
respectively. It is found that the hole trajectories contain rapid oscillations
reminiscent of the "Zitterbewegung" of relativistic electrons. We also comment
on the non-conservation of helicity of the light holes.

Mesoscale and Nanoscale Physics