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:1907.03615

Relaxation and pumping of quantum oscillator nonresonantly coupled with the other oscillator

Andrew I. Trubilko, Basharov A. M

Published Jul 8, 2019• 0 citations
arXivHTMLPDF

Abstract

The paper shows mechanisms of both the pumping and energy decay of an "isolated" oscillator. The oscillator is only non-resonantly coupled with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the "isolated" oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian, with the latter being the Hamiltonian of two oscillators and environment of one of them.

DOI
10.48550/arxiv.1907.03615

Related papers

Theory of relaxation and pumping of quantum oscillator non-resonantly coupled with the other oscillator

Andrew I. Trubilko, Ashat M. Basharov

Abstract The paper shows mechanisms of both the pumping and energy decay of an ‘isolated’ oscillator. The oscillator is only coupled non-resonantly with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the ‘isolated’ oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian. The original model is reduced to two ‘independent’ open systems, with each containing original oscillators connected with their effective independent thermal baths, whose parameters are determined. The paper also gives a description of the obtained model in terms of quantum stochastic differential equations.

Physica Scripta•Jan 22, 2020•18 citations

Nonresonant Processes as a Basis for the Formation of New Relaxation Channels in the Theory of Quantum Optical Systems

Andrew I. Trubilko, Ashat M. Basharov

Abstract The mechanisms for the pumping and decay of an “isolated” oscillator that can interact only nonresonantly with a neighboring oscillator of different frequency are presented. We show that if this neighboring oscillator is coupled to a broadband heat-bath field, the isolated oscillator begins to interact with this heat-bath field. A new relaxation channel attributable to the quantum interference of the interacting systems that is difficult or impossible to justify in terms of traditional approaches emerges as a result.

Journal of Experimental and Theoretical Physics•Jan 1, 2020•5 citations

On the Decay of an “Isolated” Oscillator Nonlinearly Coupled to a Damped Oscillator

Andrew I. Trubilko, Ashat M. Basharov

Mechanisms of pumping and decay of an “isolated” oscillator which can nonlinearly interact with a neighboring oscillator having a different frequency have been discussed. It has been shown that, if this neighboring oscillator is coupled to a broadband thermostat field, the isolated oscillator begins to interact with this thermostat field. As a result, a new relaxation channel appears because of the quantum interference of interacting systems, which can hardly be explained within traditional approaches.

Journal of Experimental and Theoretical Physics Letters•Oct 1, 2019•9 citations

Quantum kinetics and thermalization in a particle bath model

S. M. Alamoudi, D. Boyanovsky, Hector J. de Vega

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.

arXiv:cond-mat/9812029•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 1999•16 citations

Quantum Oscillator As an Open System

Andrew I. Trubilko

Abstract Using algebraic perturbation theory, the applicability of the quantum oscillator model within the theory of open quantum systems is demonstrated. The case of resonant and nonresonant interactions between two spatially separated oscillators is considered, where each oscillator interacts with its own thermostat at different temperatures. The possibility of the decay of an isolated oscillator into the thermostat of the oscillator-mediator under conditions of its nonresonant interaction with the latter is demonstrated. In all the cases presented, algebraic perturbation theory does not lead to any nonphysical features or contradictions, such as violations of the second law of thermodynamics or discrepancies in the description of these cases within the frameworks of the global and local approaches.

Moscow University Physics Bulletin•Jun 1, 2025•0 citations

Onset of non-Markovian behaviour in a harmonic oscillator stochastically coupled to a thermal bath

Santiago Velasco, Juan A. White

The influence of a finite bath correlation time and the bath temperature on the onset of a non-Markovian behaviour in the relaxation of a harmonic oscillator linearly coupled to a coloured thermal bath is analysed. A fully quantum mechanical treatment of the time autocorrelation function of the oscillator-bath interaction is made. Special attention is paid to the temperature dependence. In the low-temperature regime a non-exponential time decay of the mean number of quanta is found even though the correlation time associated with the oscillator-bath interaction is zero.

Quantum Optics Journal of the European Optical Society Part B•Aug 1, 1990•1 citation
The paper shows mechanisms of both the pumping and energy decay of an "isolated" oscillator. The oscillator is only non-resonantly coupled with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the "isolated" oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian, with the latter being the Hamiltonian of two oscillators and environment of one of them.
Abstract The paper shows mechanisms of both the pumping and energy decay of an ‘isolated’ oscillator. The oscillator is only coupled non-resonantly with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the ‘isolated’ oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian. The original model is reduced to two ‘independent’ open systems, with each containing original oscillators connected with their effective independent thermal baths, whose parameters are determined. The paper also gives a description of the obtained model in terms of quantum stochastic differential equations.
Abstract The mechanisms for the pumping and decay of an “isolated” oscillator that can interact only nonresonantly with a neighboring oscillator of different frequency are presented. We show that if this neighboring oscillator is coupled to a broadband heat-bath field, the isolated oscillator begins to interact with this heat-bath field. A new relaxation channel attributable to the quantum interference of the interacting systems that is difficult or impossible to justify in terms of traditional approaches emerges as a result.
Mechanisms of pumping and decay of an “isolated” oscillator which can nonlinearly interact with a neighboring oscillator having a different frequency have been discussed. It has been shown that, if this neighboring oscillator is coupled to a broadband thermostat field, the isolated oscillator begins to interact with this thermostat field. As a result, a new relaxation channel appears because of the quantum interference of interacting systems, which can hardly be explained within traditional approaches.
We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.
Abstract Using algebraic perturbation theory, the applicability of the quantum oscillator model within the theory of open quantum systems is demonstrated. The case of resonant and nonresonant interactions between two spatially separated oscillators is considered, where each oscillator interacts with its own thermostat at different temperatures. The possibility of the decay of an isolated oscillator into the thermostat of the oscillator-mediator under conditions of its nonresonant interaction with the latter is demonstrated. In all the cases presented, algebraic perturbation theory does not lead to any nonphysical features or contradictions, such as violations of the second law of thermodynamics or discrepancies in the description of these cases within the frameworks of the global and local approaches.
The influence of a finite bath correlation time and the bath temperature on the onset of a non-Markovian behaviour in the relaxation of a harmonic oscillator linearly coupled to a coloured thermal bath is analysed. A fully quantum mechanical treatment of the time autocorrelation function of the oscillator-bath interaction is made. Special attention is paid to the temperature dependence. In the low-temperature regime a non-exponential time decay of the mean number of quanta is found even though the correlation time associated with the oscillator-bath interaction is zero.