Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2102.13559 · Annalen der Physik

Heat Transfer and Entanglement–Non‐Equilibrium Correlation Spectra of Two Quantum Oscillators

Carsten Henkel

Published Jul 26, 2021• 0 citations
arXivHTMLPDF

Abstract

Abstract The non‐equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation‐dissipation relation is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero‐point fluctuations. No rotating‐wave approximation is applied, and anomalous heat transport from cold to hot bath, as reported in earlier work, is demonstrated not to occur.

DOI
10.1002/andp.202100089

Related papers

Heat transfer and entanglement

Carsten Henkel

The non-equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation-dissipation relation is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero-point fluctuations. No rotating-wave approximation is applied, and anomalous heat transport from cold to hot bath, as reported in earlier work, is demonstrated not to occur.

•Jul 26, 2021•2 citations

Entanglement of quantum oscillators coupled to different heat baths

Wei-Can Syu, Da-Shin Lee, Chen-Pin Yeh

Abstract We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths of quantum scalar fields at different temperature T 1 and T 2 with bilinear couplings between them. We particularly focus on the entanglement or inseparability property of their quantum states. The critical temperatures of two respective oscillators, T 1c and T 2c , higher than which the entanglement disappears, can be determined. It is found that when two damping parameters are largely different, say γ 1 ≪ γ 2 , the critical temperature T 1c with respect to the frequency Ω + , the higher frequency among two normal modes frequencies, can be very large, T 1c ≫ Ω + , while T 2c ∝ Ω + with the possibility of hot entanglement. The entanglement of two oscillators with the temperature-dependent damping parameters γ 1;2, T from heat baths is also discussed.

arXiv:2007.00288•Journal of Physics B Atomic Molecular and Optical Physics•Jan 21, 2021•5 citations

An Exact Markovian Decoherence Dynamics of Two Interacting Harmonic Oscillators Coupled to a Bosonic Heat Bath

Gábor Homa, Dávid Hamar, József Zsolt Bernád +2 more

Abstract We present an exact analytical solution of the Hu–Paz–Zhang master equation in a precise Markovian limit for a system of two harmonically coupled harmonic oscillators interacting with a common thermal bath of harmonic oscillators. The thermal bath is initially considered to be at arbitrary temperatures and characterized by an Ohmic Lorentz–Drude spectral density. In the examined system, couplings between the two harmonic oscillators and the environment ensure a complete decoupling of the center-of-mass and relative degrees of freedom, resulting in undamped dynamics in the relative coordinate. The exact time evolution is used to analyze the system’s entanglement dynamics, quantified through logarithmic negativity and quantum mutual information, while ensuring the positivity of the density operator to confirm the physical validity of the results. We demonstrate that, under certain parameter regimes and initial conditions, the asymptotic dynamics can give rise to periodic entanglement-disentanglement behavior. Furthermore, numerical simulations reveal that for negative values of the direct coupling between the oscillators, which are sufficiently close to a critical lower bound beyond which the system becomes unstable, the system can maintain entanglement across a broad temperature range and for arbitrarily long durations.

arXiv:2507.01605•Progress of Theoretical and Experimental Physics•Nov 29, 2025•1 citation

Asymptotic discord and entanglement of nonresonant harmonic oscillators under weak and strong dissipation

Luis Alfonso Correa, Antonio A. Valido, Daniel Alonso

In this work, we calculate the exact asymptotic quantum correlations between two interacting nonresonant harmonic oscillators in a common Ohmic bath. We derive analytical formulas for the covariances, fully describing any Gaussian stationary state of the system, and use them to study discord and entanglement in the strong- and weak-dissipation regimes. We discuss the rich structure of the discord of the stationary separable states arising in the strong-dissipation regime. Also under strong dissipation, when the modes are not mechanically coupled, these may entangle only through their interaction with the common environment. Interestingly enough, this stationary entanglement assisted by dissipation is only present within a finite band of frequencies and increases with the dissipation rate. Robust entanglement between detuned oscillators is also observed at low temperature.

arXiv:1111.0806•Physical Review A•Jul 20, 2012•40 citations

Nonequilibrium nonlinear open quantum systems: Functional perturbative analysis of a weakly anharmonic oscillator

Jen-Tsung Hsiang, B. L. Hu

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.

arXiv:1912.12803•Physical review. D/Physical review. D.•Jun 2, 2020•14 citations

On the localized quantum oscillators in a common heat bath

Z. Nasr, Fardin Kheirandish

To remedy the failure of minimal coupling method in describing the quantum dynamics of two localized Brownian oscillators interacting with a common medium, a scheme is introduced to model the medium by a continuum of complex scalar fields or equivalently two independent real scalar fields. The starting point is a Lagrangian of the total system and quantization is achieved in the framework of canonical quantization. The equations of motion, memory or response functions and fluctuation–dissipation relations are obtained. An induced force between oscillators is obtained originating from the fluctuations of the medium. Ohmic and non-Ohmic regimes are discussed and the positions of oscillators are obtained approximately in large time limit and weak coupling regime. Quantum entanglement between localized oscillators is obtained in zero temperature and strong coupling regime.

arXiv:1612.07675•International Journal of Modern Physics B•Mar 23, 2017•1 citation
Abstract The non‐equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation‐dissipation relation is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero‐point fluctuations. No rotating‐wave approximation is applied, and anomalous heat transport from cold to hot bath, as reported in earlier work, is demonstrated not to occur.
The non-equilibrium state of two oscillators with a mutual interaction and coupled to separate heat baths is discussed. Bosonic baths are considered, and an exact spectral representation for the elements of the covariance matrix is provided analytically. A wide class of spectral densities for the relevant bath modes is allowed for. The validity of the fluctuation-dissipation relation is established for global equilibrium (both baths at the same temperature) in the stationary state. Spectral measures of entanglement are suggested by comparing to the equilibrium spectrum of zero-point fluctuations. No rotating-wave approximation is applied, and anomalous heat transport from cold to hot bath, as reported in earlier work, is demonstrated not to occur.
Abstract We study the non-equilibrium dynamics of two coupled oscillators interacting with their own heat baths of quantum scalar fields at different temperature T 1 and T 2 with bilinear couplings between them. We particularly focus on the entanglement or inseparability property of their quantum states. The critical temperatures of two respective oscillators, T 1c and T 2c , higher than which the entanglement disappears, can be determined. It is found that when two damping parameters are largely different, say γ 1 ≪ γ 2 , the critical temperature T 1c with respect to the frequency Ω + , the higher frequency among two normal modes frequencies, can be very large, T 1c ≫ Ω + , while T 2c ∝ Ω + with the possibility of hot entanglement. The entanglement of two oscillators with the temperature-dependent damping parameters γ 1;2, T from heat baths is also discussed.
Abstract We present an exact analytical solution of the Hu–Paz–Zhang master equation in a precise Markovian limit for a system of two harmonically coupled harmonic oscillators interacting with a common thermal bath of harmonic oscillators. The thermal bath is initially considered to be at arbitrary temperatures and characterized by an Ohmic Lorentz–Drude spectral density. In the examined system, couplings between the two harmonic oscillators and the environment ensure a complete decoupling of the center-of-mass and relative degrees of freedom, resulting in undamped dynamics in the relative coordinate. The exact time evolution is used to analyze the system’s entanglement dynamics, quantified through logarithmic negativity and quantum mutual information, while ensuring the positivity of the density operator to confirm the physical validity of the results. We demonstrate that, under certain parameter regimes and initial conditions, the asymptotic dynamics can give rise to periodic entanglement-disentanglement behavior. Furthermore, numerical simulations reveal that for negative values of the direct coupling between the oscillators, which are sufficiently close to a critical lower bound beyond which the system becomes unstable, the system can maintain entanglement across a broad temperature range and for arbitrarily long durations.
In this work, we calculate the exact asymptotic quantum correlations between two interacting nonresonant harmonic oscillators in a common Ohmic bath. We derive analytical formulas for the covariances, fully describing any Gaussian stationary state of the system, and use them to study discord and entanglement in the strong- and weak-dissipation regimes. We discuss the rich structure of the discord of the stationary separable states arising in the strong-dissipation regime. Also under strong dissipation, when the modes are not mechanically coupled, these may entangle only through their interaction with the common environment. Interestingly enough, this stationary entanglement assisted by dissipation is only present within a finite band of frequencies and increases with the dissipation rate. Robust entanglement between detuned oscillators is also observed at low temperature.
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.
To remedy the failure of minimal coupling method in describing the quantum dynamics of two localized Brownian oscillators interacting with a common medium, a scheme is introduced to model the medium by a continuum of complex scalar fields or equivalently two independent real scalar fields. The starting point is a Lagrangian of the total system and quantization is achieved in the framework of canonical quantization. The equations of motion, memory or response functions and fluctuation–dissipation relations are obtained. An induced force between oscillators is obtained originating from the fluctuations of the medium. Ohmic and non-Ohmic regimes are discussed and the positions of oscillators are obtained approximately in large time limit and weak coupling regime. Quantum entanglement between localized oscillators is obtained in zero temperature and strong coupling regime.