On dynamical stochasticity in nonlinear quantum systems

The properties of nonlinear quantum systems which are stochastic in the classical limit are investigated. By a concrete model example it is shown that for a quantum system in contrast to the corresponding classical one the Kolmogorov-Sinai (KS) entropy is equal to zero and correlations are damping not by exponential but only but power-type law. It is pointed out in conclusion that the cause of power-type correlation decrease is power-type increase of THETA harmonics number in U with time (U is evolution operator) or in other words of a number of populated levels of the unperturbed system (one impact captures approximately 2 K levels of unperturbed system ). In view of this fact the THETA number of harmonics also grows by power-type law which leads to h=C and nonexponential correlation damping. As the indicated U property occurs prractically for all perturbations it is quite natural to expect that the other quantum systems, which are stochastical in the classical limit are to possess KS entropy equal to zero and power-type correlation decrease. This result indicates that direct generalization of Kolmogorov entropy notion for quantum systems seems to be not so important as in classical systems