  We report equations of motion for the occupation numbers of natural spin
orbitals and show that adiabatic extensions of common functionals employed in
ground-state reduced-density-matrix-functional theory have the shortcoming of
leading always to occupation numbers which are independent of time. We
illustrate the exact time-dependence of the natural spin orbitals and
occupation numbers for the case of electron-ion scattering and for atoms in
strong laser fields. In the latter case, we observe strong variations of the
occupation numbers in time.
