Heat conduction in quantum harmonic chains with alternate masses and self-consistent thermal reservoirs

Neto, Antônio Francisco; Lemos, Humberto C. F.; Pereira, Emmanuel

doi:10.1103/physreve.76.031116

Cited by 16 publications

(12 citation statements)

References 27 publications

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“…heat transfer is diffusive [22][23][24][25]. SCTB model has also been applied to investigating quantum effects in non-ballistic heat transfer [24][25][26][27], effects of additional anharmonicity [23,[28][29][30] and unequal masses [31][32][33] on heat conduction and the necessary ingredients of thermal rectification [27,[34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths

2013

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Modeling of thermal transport in practical nanostructures requires making trade-offs between the size of the system and the completeness of the model. We study quantum heat transfer in a selfconsistent thermal bath setup consisting of two lead regions connected by a center region. Atoms both in the leads and in the center region are coupled to quantum Langevin heat baths that mimic the damping and dephasing of phonon waves by anharmonic scattering. This approach treats the leads and the center region on same footing and thereby allows for a simple and physically transparent thermalization of the system, enabling also perfect acoustic matching between the leads and the center region. Increasing the strength of the coupling reduces the mean free path of phonons and gradually shifts phonon transport from ballistic regime to diffusive regime. In the center region, the bath temperatures are determined self-consistently from the requirement of zero net energy exchange between the local heat bath and each atom. By solving the stochastic equations of motion in frequency space and averaging over noise using the general fluctuation-dissipation relation derived by Dhar and Roy [J. Stat. Phys. 125, 801 (2006)], we derive the formula for thermal current, which contains the Caroli formula for phonon transmission function and reduces to the Landauer-Büttiker formula in the limit of vanishing coupling to local heat baths. We prove that the bath temperatures measure local kinetic energy and can, therefore, be interpreted as true atomic temperatures. In a setup where phonon reflections are eliminated, Boltzmann transport equation under gray approximation with full phonon dispersion is shown to be equivalent to the self-consistent heat bath model. We also study thermal transport through two-dimensional constrictions in square lattice and graphene and discuss the differences between the exact solution and linear approximations.

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Section: Introductionmentioning

confidence: 99%

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths

2013

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“…More recently, the model was revisited by Roy and Dhar [20,21], who demonstrated that under the linear response assumption and for asymptotically long chains, Fourier's law holds and a temperature dependent thermal conductivity is realized. An analytical study of the SC model with alternate masses has revealed the role of quantum effects at low temperatures [22,23]. More recently, a mathematical analysis of the mass-graded SC model in the quantum domain has indicated on the onset of thermal rectification, beyond the linear response regime [24].…”

Section: Introductionmentioning

confidence: 99%

Quantum heat transfer in harmonic chains with self-consistent reservoirs: Exact numerical simulations

Bandyopadhyay

Segal

2011

Phys. Rev. E

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We describe a numerical scheme for exactly simulating the heat current behavior in a quantum harmonic chain with self-consistent reservoirs. Numerically-exact results are compared to classical simulations and to the quantum behavior under the linear response approximation. In the classical limit or for small temperature biases our results coincide with previous calculations. At large bias and for low temperatures the quantum dynamics of the system fundamentally differs from the closeto-equilibrium behavior, revealing in particular the effect of thermal rectification for asymmetric chains. Since this effect is absent in the classical analog of our model, we conclude that in the quantum model studied here thermal rectification is a purely quantum phenomenon, rooted in the quantum statistics.

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“…Anyway, even if we discard any relation with anharmonicity, these results show, at least, that the onset of Fourier's law does not guarantee thermal rectification in asymmetric classic models -we recall that the Fourier's law does not hold in standard harmonic systems (i.e., harmonic models with reservoirs at the boundaries only), but it holds in the SC models.Still searching for the mechanism behind the rectification in graded mass systems, we recall that, at low temperatures, quantum effects may introduce significant changes. The thermal conductivity for the quantum self-consistent harmonic chain (QSC), for example, depends on temperature [8,26], in opposition to the CSC thermal conductivity [7]. Thus, searching for possible quantum effects in the mechanism of thermal rectification, in a quite recent work [27], we turn to the inhomogeneous QCS and, in the linear response regime, i.e., for the chain submitted to a very small gradient of temperature and considering only linear corrections in computations with changes in the temperature, we show the absence of thermal rectification despite quantum effects in the conductivity.…”

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confidence: 99%

“…( 4) and necessary to study F l , may be a very difficult task -we know a precise solution for some specific cases: e.g., for a homogeneous next-neighbors interparticle interaction and all particles with the same mass M W = mI [8]; and also for the case of particles with alternate masses, i.e. m j = m 1 for j odd, and m j = m 2 for j even [26]. Hence, we first restrict our interparticle interaction Φ to the homogeneous nearestneighbor case, i.e., Φ = −∆, the lattice Laplacian, and study the equations for the smallest possible chain: N = 3 (it is, in fact, a cell of a large chain).…”

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confidence: 99%

Thermal rectification in quantum graded mass systems

Pereira

2010

Physics Letters A

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We show the existence of thermal rectification in the graded mass quantum chain of harmonic oscillators with self-consistent reservoirs. Our analytical study allows us to identify the ingredients leading to the effect. The presence of rectification in this effective, simple model (representing graded mass materials, systems that may be constructed in practice) indicates that rectification in graded mass quantum systems may be an ubiquitous phenomenon. Moreover, as the classical version of this model does not present rectification, our results show that, here, rectification is a direct result of the quantum statistics. A fundamental challenge in statistical physics is the derivation of macroscopic phenomenological laws of thermodynamic transport from the underlying microscopic Hamiltonian systems. However, after decades, a first-principle derivation of the Fourier's law of heat conduction, for instance, is still a puzzle [1]. Many works have been devoted to the theme [2], most of them by means of computer simulations. But, in these problems where the central question involves the convergence or divergence of thermal conductivity, sometimes there is a significant difficulty to arrive at precise conclusions from numerical results [3]. Thus, the necessity of analytical studies together with the huge complexity of the associated nonlinear dynamical systems led to several works considering approximative schemes or simplified models [4] -since the pioneering work of Debye, the microscopic models to describe heat conduction are mainly given by systems of anharmonic oscillators, leading to problems without analytical solutions. Many works involve, e.g., the use of approximations such as Boltzmann equations, master equations for effective models, the analysis of Green-Kubo formula, etc. An example of simple (effective) model that can be analytically studied is the classical or quantum harmonic chain of oscillators with self-consistent reservoirs. It has been proposed a while ago [5,6], but it is always revisited [7,8]. In such model, each site of the chain is coupled to a reservoir; the first and last sites are coupled to "real" thermal baths, while the inner reservoirs only mimic the absent anharmonic interactions. The self-consistent condition means that there is no heat flow between an inner reservoir and its site in the steady state: the inner baths act only as a phonon scattering mechanism, such as 1

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Heat conduction in quantum harmonic chains with alternate masses and self-consistent thermal reservoirs

Cited by 16 publications

References 27 publications

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths

Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths

Quantum heat transfer in harmonic chains with self-consistent reservoirs: Exact numerical simulations

Thermal rectification in quantum graded mass systems

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