Bistability in quantum nonlinear oscillator excited by stochastic force

TL;DR

This paper develops an analytical approach to identify multiple stationary states in a quantum nonlinear oscillator driven by stochastic forces, revealing conditions for bistability through stability analysis.

Contribution

It introduces an approximate analytical method to analyze stationary states and bistability in quantum nonlinear oscillators under noise, considering phase fluctuations.

Findings

Identified parameter regions with multiple stationary solutions.

Derived a nonlinear integral equation for the oscillator's mean energy.

Performed linear stability analysis of stationary states.

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.