  We consider the simplest example of a nonstationary quantum system which is
quantum mechanical oscillator with varying frequency and $\lambda \phi^4$
self-interaction. We calculate loop corrections to the Keldysh,
retarded/advanced propagators and vertices using Schwinger--Keldysh
diagrammatic technique and show that there is no physical secular growth of the
loop corrections in the cases of constant and adiabatically varying frequency.
This fact corresponds to the well-known adiabatic theorem in quantum mechanics.
However, in the case of non-adiabatically varying frequency we obtain strong IR
corrections to the Keldysh propagator which come from the `sunset' diagrams,
grow with time indefinetely and indicate energy pumping into the system. It
reveals itself via the change in time of the level population and of the
anomalous quantum average.
