  It is shown that a periodic perturbation of the quantum pendulum (similarly
to the classical one) in the neighbourhood of the separatrix can bring about
irreversible phenomena. As a result of recurrent passages between degenerate
states, the system gets self-chaotized and passes from the pure state to the
mixed one. Chaotization involves the states, the branch points of whose levels
participate in a slow "drift" of the system along the Mathieu characteristics
this "drift" being caused by a slowly changing variable field. Recurrent
relations are obtained for populations of levels participating in the
irreversible evolution process. It is shown that the entropy of the system
first grows and, after reaching the equilibrium state, acquires a constant
value.
