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The presentation contains a summary of the talk and a few additional applications with references which were skipped due to time limitations, in particular:

1. transparancies 21-24 an example how to derive quantum kinetic equations from the two-time NEGF. The example shows a gauge-invariant derivation of the collision integral of an electron-ion plasma in the presence of a monochromotic field (optical to x-ray). The result includes multiphoton absorption and inverse bremsstrahlung heating of electrons.

2. 25-27: numerical solution of the derived kinetic equation for an electron-ion plasma in a strong field, including harmonics generation.

3. 28 demonstration of total energy conservation - observed by full solution of the two-time Keldysh-Kadanoff-Baym equations (KBE) for the NEGF. This is in contrast to Boltzmann type (Markovian) kinetic equations which conserve only kinetic energy, transparancy 29.

4. 30-31 Solution of the KBE for a two band semiconductor under optical excitation.

5. 32-34 Solution of the KBE for an inhomogeneous electron gas which yields the dynamic structure factor including correlations and vertex corrections in a sum rule preserving fashion.

Comment on the density operator: