Condition of stochasticity in quantum nonlinear systems

The transition from dynamical (regular) to stochastical behaviour in nonlinear quantum systems is considered. A method of describing the stochastical instability is proposed for quantum systems. The method is based on the determination of a discrete time mapping of the creation and annihilation operators in the Heisenberg picture and the projection of this mapping on the phase space of coherent states. The condition that the phase correlation vanishes is found for a nonlinear quantum oscillator perturbed by the external periodical force, which is a linear combination of delta pulses. The kinetic equation describing the relaxation of the system in the space of c-numbers formed by the projections of the operators is derived.