Condition of stochasticity in quantum nonlinear systems

Quantum K-systems can usually be regarded as the systems which are conventional K-systems at ℏ = 0, i.e. they have the property of mixing trajectories in a phase space. The master kinetic equation without a priori random phase assumptions is derived in the quasiclassical approximation for the quantum K-systems. It is shown how the nondiagonal elements of density matrix decay and the memory about initial conditions vanishes. A quantum nonlinear oscilator perturbed by a periodically time-dependent field is considered as an example.