Thermal transport in out-of-equilibrium quantum harmonic chains

Nicacio, F.; Ferraro, Alessandro; Imparato, Alberto; Paternostro, Mauro; Semião, F. L.

doi:10.1103/physreve.91.042116

Cited by 43 publications

(49 citation statements)

References 15 publications

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“…The work in this section extends the treatments of [5] and [40] to the case where the N oscillators do not interact directly, but via coupling to a common, adiabatically eliminated, mode. To proceed further, one needs an expression for the average occupation of the mechanical elements.…”

Section: Heat Flow For N Oscillators Coupled To a Common Oscillator Amentioning

confidence: 96%

“…We show that, after the adiabatic elimination of the field, it is equivalent to a generic two-oscillator system with an effective mutual linear coupling, an effective common bath and two independent baths (sections 4.1 and 4.2). We solve this generic problem for thermal Markovian baths and derive expressions, equations (39) and (40), for the steady state occupation and heat flows of the mechanics. In section 4.3, we discuss the results in various parameter regimes which could be realized through a suitable engineering of the optomechanical interaction and give an indication of the various systems that could be used for investigating the effects we explore.…”

Section: Introductionmentioning

confidence: 99%

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Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

2015

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We investigate the transport of phonons between N harmonic oscillators in contact with independent thermal baths and coupled to a common oscillator, and derive an expression for the steady state heat flow between the oscillators in the weak coupling limit. We apply these results to an optomechanical array consisting of a pair of mechanical resonators coupled to a single quantized electromagnetic field mode by radiation pressure as well as to thermal baths with different temperatures. In the weak coupling limit this system is shown to be equivalent to two mutually-coupled harmonic oscillators in contact with an effective common thermal bath in addition to their independent baths. The steady state occupation numbers and heat flows are derived and discussed in various regimes of interest.

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Section: Heat Flow For N Oscillators Coupled To a Common Oscillator Amentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

2015

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“…(See the appendix C or [36][37][38][39] for the derivation.) From here, the application of the map in an infinitesimal time δt can be identified as:…”

Section: Fdt For Lindbladian Master Equationsmentioning

confidence: 99%

Linear response theory for quantum Gaussian processes

2019

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Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.

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“…The stochastic covariance part simplifies, under the initial conditions we have assumed, as Inserting the formal solution of (15),…”

Section: Deterministic Evolution Of the Split Covariance Termsmentioning

confidence: 99%

“…Weak system-bath interactions at low temperatures induce correlations between system and reservoir, which lead to non-negligible energy exchange [9] and produce unphysical results in conventional perturbative treatments [10,11]. Moreover, the relaxation towards stationary states at low temperatures generally depends on the nature of the surrounding heat baths and, particularly, on non-Markovian dynamics [12][13][14][15]. Since harmonic systems allow for exact results at least in principle, they may on the one hand serve as non-trivial paradigmatic examples and, on the other hand, as starting points for more elaborate models.…”

Section: Introductionmentioning

confidence: 99%

Currents and fluctuations of quantum heat transport in harmonic chains

2017

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Heat transport in open quantum systems is particularly susceptible to the modeling of systemreservoir interactions. It thus requires us to consistently treat the coupling between a quantum system and its environment. While perturbative approaches are successfully used in fields like quantum optics and quantum information, they reveal deficiencies-typically in the context of thermodynamics, when it is essential to respect additional criteria such as fluctuation-dissipation theorems. We use a non-perturbative approach for quantum dissipative dynamics based on a stochastic Liouville-von Neumann equation to provide a very general and extremely efficient formalism for heat currents and their correlations in open harmonic chains. Specific results are derived not only for firstbut also for second-order moments, which requires us to account for both real and imaginary parts of bath-bath correlation functions. Spatiotemporal patterns are compared with weak coupling calculations. The regime of stronger system-reservoir couplings gives rise to an intimate interplay between reservoir fluctuations and heat transfer far from equilibrium.

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Thermal transport in out-of-equilibrium quantum harmonic chains

Cited by 43 publications

References 15 publications

Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

Linear response theory for quantum Gaussian processes

Currents and fluctuations of quantum heat transport in harmonic chains

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