Bistability in quantum nonlinear oscillator excited by stochastic force

Abstract

We present approximate analytical method of analysis of stationary states of nonlinear quantum systems with the noise. As an example we consider quantum nonlinear oscillator excited by fluctuating force and found parameter regions with more than one stationary solutions. Existence of such region is the necessary condition for bistability. We neglect by fluctuations in the amplitude of oscillations but do not neglect by fluctuations in its phase. Then oscillator noise power spectrum depends on oscillator mean energy n, which leads to nonlinear integral equation for n. Analytical solution of this equation can be found. Stationary states of the oscillator are found for various spectrums of fluctuations of the exciting force. Linear stability analysis of stationary states was carried out.