Quantum dissipative dynamics of driven Duffing oscillator near attractors

TL;DR

This paper develops a refined perturbation theory to analyze quantum dissipative dynamics of a driven Duffing oscillator near attractors, revealing how damping and quantum effects influence level spacings and effective temperature.

Contribution

It introduces a novel perturbative approach that accounts for multiple small parameters, providing analytical insights beyond standard linearization for quantum Duffing oscillators near stable states.

Findings

Strong damping causes additional renormalization of level spacings.

Quantum effects and dephasing influence the effective temperature.

The framework applies to quantum systems near stable states.

Abstract

We investigate the quantum dissipative dynamics near the stable states (attractors) of a driven Duffing oscillator. A refined perturbation theory that can treat two perturbative parameters with different orders is developed to calculate the quantum properties of the Duffing oscillator near the attractors. We obtain the perturbative analytical results, that go beyond the standard linearization approach, for the renormalized level spacings, the orbital displacements, and the effective temperature near the classical attractor. Furthermore, we demonstrate that strong damping induces additional slight renormalization of level spacings, and the Bose distribution together with dephasing. Our work provides new insights into the quantum dynamics of the driven Duffing oscillator and offers a theoretical framework that can be applied to related quantum systems near their stable states.