Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator

TL;DR

This paper develops a perturbative approach to analyze weakly nonlinear open quantum systems, specifically a quantum anharmonic oscillator coupled to a heat bath, revealing fluctuation-dissipation relations and energy flow characteristics.

Contribution

It introduces a functional perturbative method for weakly nonlinear open quantum systems and connects fluctuation-dissipation relations with nonequilibrium dynamics.

Findings

Derived covariance matrix and correlation functions for the anharmonic oscillator.

Identified a fluctuation-dissipation relation in the nonequilibrium setting.

Linked energy flow patterns to the existence of equilibrium states.

Abstract

We introduce a functional perturbative method for treating weakly nonlinear systems coupled with a quantum field bath. We demonstrate using this method to obtain the covariance matrix elements and the correlation functions of a quantum anharmonic oscillator interacting with a heat bath. We identify a fluctuation-dissipation relation based on the nonequilibrium dynamics of this nonlinear open quantum system. To establish its connection with dynamical equilibration, we further examine the energy flows between the anharmonic oscillator and the bath field. The vanishing of the net flow {is an indication of} the existence of an equilibrium state for such an open-system configuration. The results presented here are useful for studying the nonequilibrium physical processes of nonlinear quantum systems such as heat transfer or electron transport.