Quantum damped nonstationary oscillator and Dynamical Casimir Effect

I consider the model of quantum damped oscillator with time-dependent frequency and damping coefficients, which can be used to predict the results of current experiments aimed at the discovering the so-called Dynamical Casimir Effect. It is based on the Heisenberg-Langevin approach to the description of open quantum systems. The main emphasis is made on the comparison of the exactly solvable special cases with general approximate solutions found earlier. The examples considered demonstrate that simple approximate formulas are quite reliable for the analysis of realistic experimental situations.