We discuss the spin and charge dynamics of conduction-band electrons in semiconductor systems with k-linear spin-orbit splitting. The temporal and spatial fluctuations of spin density emerging in the system are correlated and the correlations drastically increase in the regime of persistent spin helix. In the presence of the Zeeman gap, opened by a magnetic field, the electrons experience trembling motion, similar to Zitterbewegung of relativistic particles. The trembling motion of individual electrons can be phase-synchronized by initializing the electrons in the same spin state and detected as a macroscopic high-frequency electric current.