Time-dependent quantum damped oscillator with 'minimal noise': application to the nonstationary Casimir effect in nonideal cavities

We consider a consistent model of a quantum damped harmonic oscillator with arbitrary time-dependent frequency and damping coefficients in the frameworks of the Heisenberg-Langevin equations with two noncommuting delta-correlated noise operators. For the 'minimal noise' set of correlation functions, which have the same time dependence as the damping coefficient, we obtain the exact solution, which is the generalization of Husimi's solution for the undamped nonstationary oscillator. The model is applied to the problem of the photon creation from vacuum or thermal states due to the nonstationary Casimir effect inside the cavity with periodical time-dependent conductivity of the thin semiconductor boundary layer, simulating the periodical displacements of the wall. The general formula for the rate of photon generation under the resonance conditions in the presence of dissipation is obtained.