Semiclassical time evolution of the holes from Luttinger Hamiltonian

We study the semiclassical 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 nonabelian adiabatic theories in S. Murakami, N. Nagaosa, and S. C. Zhang, 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 nonconservation of helicity of the light holes.