  We prove that if the two-body terms in the equation of motion for the
one-body reduced density matrix are approximated by ground-state functionals,
the eigenvalues of the one-body reduced density matrix (occupation numbers)
remain constant in time. This deficiency is related to the inability of such an
approximation to account for relative phases in the two-body reduced density
matrix. We derive an exact differential equation giving the functional
dependence of these phases in an interacting Landau-Zener model and study their
behavior in short- and long-time regimes. The phases undergo resonances
whenever the occupation numbers approach the boundaries of the interval [0,1].
In the long-time regime, the occupation numbers display correlation-induced
oscillations and the memory dependence of the functionals assumes a simple
form.
