  We discuss some problems of dissipative chaos for open quantum systems in the
framework of semiclassical and quantum distributions. For this goal, we propose
a driven nonlinear oscillator with time-dependent coefficients, i.e. with
time-dependent Kerr-nonlinearity and time-modulated driving field. This model
showing both regular and chaotic dynamics in the classical limit is realized in
several experimental schemes. Quantum dissipative chaos is analyzed on the base
of numerical method of quantum trajectories. Three quantities are studied: the
Wigner function of oscillatory mode from the point of view of quantum-assemble
theory and both semiclassical Poincare section and quantum Poincare section
calculated on a single quantum trajectory. The comparatively analysis of these
distributions for various operational chaotic regimes of the models is
performed, as well as scaling invariance in dissipative chaos and quantum
interference effects assisted by chaos are discussed.
