Dissipation of classical energy in nonlinear quantum systems

Time dependence of energy transfer from classical to quantum reservoir in nonlinear system is considered. Classical energy is understood as the part of system energy that is expressible through average values of coordinates and momenta. Dissipation of classical energy is studied in exactly solvable Jaynes-Cummings model. This process is also investigated using numerical and approximate analytical approaches in a simple nonlinear oscillator model.