  The time evolution of optically excited carriers in semiconductor quantum
wells and quantum dots is analyzed for their interaction with LO-phonons. Both
the full two-time Green's function formalism and the one-time approximation
provided by the generalized Kadanoff-Baym ansatz are considered, in order to
compare their description of relaxation processes. It is shown that the
two-time quantum kinetics leads to thermalization in all the examined cases,
which is not the case for the one-time approach in the intermediate-coupling
regime, even though it provides convergence to a steady state. The
thermalization criterion used is the Kubo-Martin-Schwinger condition.
