Thermal conductivity of anharmonic crystals with self-consistent baths: Analytical computation with discrete time

Pereira, Emmanuel; Falcao, Ricardo; Lemos, Humberto C. F.

doi:10.1103/physreve.87.032158

Cited by 12 publications

(11 citation statements)

References 27 publications

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“…the computations presented in Ref. [22]. In short, the heat current expressions above shall be valid even for some cases of anharmonic chains without inner reservoirs.…”

Section: Model and Approachmentioning

confidence: 97%

Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

Ávila

Pereira

Teixeira

2015

Physica A: Statistical Mechanics and its Applications

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“…the computations presented in Ref. [22]. In short, the heat current expressions above shall be valid even for some cases of anharmonic chains without inner reservoirs.…”

Section: Model and Approachmentioning

confidence: 97%

Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

Ávila

Pereira

Teixeira

2015

Physica A: Statistical Mechanics and its Applications

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“…In the limit of vanishing couplings to local heat baths, γ → 0 + , γ I → 0 + , the lead and center region Green's functions ( 8) and ( 14) region reduce to their ballistic counterparts and the only non-zero transmission function is T LR (ω). Equation (30)…”

Section: Heat Flow To Bathsmentioning

confidence: 99%

“…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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“…To infer the behavior of F j,ℓ , we turn to Ref. [19], where a huge similarity between the anharmonic self-consistent chain and the anharmonic chain with baths only at the ends is pointed out, at least for large anharmonicity. We remark that expressions for κ have been already precisely derived for some models.…”

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confidence: 99%

Increasing thermal rectification: Effects of long-range interactions

Pereira

Ávila

2013

Phys. Rev. E

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In this paper, we study the effects of the interparticle interaction range on heat flow. We show that, by increasing the interaction range, we may amplify the thermal conductivity and even change the regime of heat transport. More importantly, considering a crucial problem of phononics, namely, the search of a suitable thermal diode, we investigate the range effects in some graded systems in which thermal rectification is a ubiquitous phenomenon. In such graded models, we show that long range interactions may significatively increase the rectification power and may avoid its decay with the system size, thus solving relevant problems of the usual proposals of rectifiers. Our results indicate that graded materials are genuine candidates for the actual fabrication of thermal diodes. The invention of transistor used to control the electric charge flow has led to the incredible development of modern electronics. Now we observe the progress of phononics [1], the counterpart of electronics dedicated to the manipulation and control of heat current. However, a very promising advance is still dependent on the development of one of its basic component: a realizable thermal diode with a significative rectification. A thermal diode, or rectifier, is a device in which heat flows preferably in one direction, i.e., the magnitude of the heat current changes if we invert the device between two thermal baths.A model of thermal rectifier has been proposed some time ago [2], and since then, thermal rectification has been intensively investigated [3][4][5][6][7][8][9][10], including experimental realizations [6]. Unfortunately, the most recurrent proposals of thermal diode, which are based on the sequential coupling of two or three segments with different anharmonic potentials, are difficult to be experimentally implemented and their rectification power typically decays to zero when we increase the system size [4]. For these reasons, more and more efforts have been devoted to the investigation of rectification in different models [5][6][7][8]: for example, in graded systems (in which rectification is a ubiquitous phenomenon [9, 10]), in carbon nano-structures, in systems composed of crystal and amorphous polymer, etc. Graded materials are inhomogeneous systems whose composition and/or structure change gradually in space. It is worth to stress that such materials are abundant in nature, can also be manufactured, and have attracted great interest in many areas [11], with works devoted to the study of their electric, optical, mechanical and heat conduction properties.In the search for mechanisms which may increase the rectification power, and/or avoid its rapid decay with the system size, the present work is devoted to a basic, but somehow neglected problem: the effects of the interpar- * Electronic address: emmanuel@fisica.ufmg.br; rravila@fisica.ufmg.br ticle interaction range on the heat flow properties. Given the enormous mathematical difficulty of the usual models considered in the study of heat conduction in solids, models which a...

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Thermal conductivity of anharmonic crystals with self-consistent baths: Analytical computation with discrete time

Cited by 12 publications

References 27 publications

Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

Length dependence of heat conduction in (an)harmonic chains with asymmetries or long range interparticle interactions

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

Increasing thermal rectification: Effects of long-range interactions

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