Time-dependent natural orbitals and occupation numbers

Using the equations of motion for the occupation numbers of natural spin orbitals we show that adiabatic extensions of common functionals employed in ground-state reduced-densitymatrix-functional theory have the shortcoming of leading to occupation numbers independent of time. We illustrate the exact time-dependence of the natural spin orbitals and occupation numbers for two strongly nonlinear cases, namely electron-ion scattering and atoms in strong laser fields. In the latter case, we observe strong variations of the occupation numbers in time.