Nonequilibrium Steady State in Open Quantum Systems: Influence Action, Stochastic Equation and Power Balance

Abstract

The existence and uniqueness of a steady state for nonequilibrium systems (NESS) is a fundamental subject and a main theme of research in statistical mechanics for decades. For Gaussian systems, such as a chain of harmonic oscillators connected at each end to a heat bath, and for anharmonic oscillators under specified conditions, definitive answers exist in the form of proven theorems. Answering this question for quantum many-body systems poses a challenge for the present. In this work we address this issue by deriving the stochastic equations for the reduced system with self-consistent backaction from the two baths, calculating the energy flow from one bath to the chain to the other bath, and exhibiting a power balance relation in the total (chain + baths) system which testifies to the existence of a NESS in this system at late times. Its insensitivity to the initial conditions of the chain corroborates to its uniqueness. The functional method we adopt here entails the use of the influence functional, the coarse-grained and stochastic effective actions, from which one can derive the stochastic equations and calculate the average values of physical variables in open quantum systems. This involves both taking the expectation values of quantum operators of the system and the distributional averages of stochastic variables stemming from the coarse-grained environment. This method though formal in appearance is compact and complete. It can also easily accommodate perturbative techniques and diagrammatic methods from field theory. Taken all together it provides a solid platform for carrying out systematic investigations into the nonequilibrium dynamics of open quantum systems and quantum thermodynamics.

75 pages. Missing references in v1 fixed. Apologies

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Cited by in corpus (28)

• Keldysh Field Theory for Driven Open Quantum Systems
• Harnessing symmetry to control quantum transport
• Steady-state entanglement and coherence of the coupled qubit system in equilibrium and nonequilibrium environments
• Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law
• Nonequilibrium Thermodynamics of Quantum Friction
• Coherence enhanced quantum metrology in a nonequilibrium optical molecule
• Thermodynamics of quantum systems strongly coupled to a heat bath I. Operator thermodynamic functions and relations
• Power law tails and non Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory
• Fluctuation-Dissipation Relation from the Nonequilibrium Dynamics of a Nonlinear Open Quantum System
• Theory of Entropy Production in Quantum Many-Body Systems
• Fluctuation-Dissipation and Correlation-Propagation Relations from the Nonequilibrium Dynamics of Detector-Quantum Field Systems
• Quantum Entanglement at High Temperatures? II. Bosonic Systems in Nonequilibrium Steady State
• Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator
• Variational Quantum Algorithms for Steady States of Open Quantum Systems
• Fluctuation-Dissipation and Correlation-Propagation Relations in $(1+3)$D Moving Detector-Quantum Field Systems
• "Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny
• Entanglement dynamics of coupled quantum oscillators in independent nonMarkovian baths
• Fluctuation-Dissipation Relation for Open Quantum Systems in Nonequilibrium Steady State
• Nonequilibrium Steady State and Heat Transport in Nonlinear Open Quantum Systems: Stochastic Influence Action and Functional Perturbative Analysis
• Quantum Thermodynamic Uncertainty Relations, Generalized Current Fluctuations and Nonequilibrium Fluctuation-Dissipation Inequalities
• Entanglement of quantum oscillators coupled to different heat baths
• Hot entanglement? -- Parametrically coupled quantum oscillators in two heat baths: instability, squeezing and driving
• Quantum Thermodynamic Uncertainties in Nonequilibrium Systems from Robertson-Schrödinger Relations
• Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'
• Atom-Field-Medium Interactions I: Graded Influence Actions for $N$ Harmonic Atoms in a Dielectric-Altered Quantum Field
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Heat transfer and entanglement -- non-equilibrium correlation spectra of two quantum oscillators
• Fluctuation-Dissipation Relation for a Quantum Brownian Oscillator in a Parametrically Squeezed Thermal Field