Quantum approach by the Lindblad master equation to the autonomous oscillator in hard excitation regime

Abstract

We propose the simple quantum model of nonlinear autonomous oscillator in hard excitation regime. We originate from classical equations of motion for similar oscillator and quantize them using the Lindblad master equation for the density matrix of this system. The solution for the populations of the stationary states of such oscillator may be explicitly found in the case when nonlinearity parameters of the problem are small. It was shown that in this situation there are three distinct regimes of behavior of the model. We compare properties of this model with corresponding ones of another closely connected open system, namely quantum oscillator in soft excitation regime. We discuss a possible applications of the results obtained.