Effective classical harmonic crystal with thermal rectification
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 95-105 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the existence of a thermal rectification mechanism in a harmonic model with a temperature-dependent effective potential. In contrast to much earlier work where it was shown for this model that rectification occurs in short chains of up to six sites, we analytically prove that this phenomenon occurs in a material with graded mass distribution for any size of the chain and is independent of the regime of heat transport. We find that thermal rectification is observed in a system with other asymmetric parameters, which can be related to structure parameters of the system or to features that depend on the temperatures of the internal sites of the chain and change when the heat baths at ends of the chain exchange places. The description of thermal rectification in these simplified models with a minimal set of ingredients shows that the phenomenon is ubiquitous and can help to theoretically investigate and practically create an efficient thermal diode.
Mots-clés : thermal diode, rectifier
Keywords: heat flux, harmonic model.
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S. H. C. Silva. Effective classical harmonic crystal with thermal rectification. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 1, pp. 95-105. http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a5/

[1] R. Paierls, Kvantovaya teoriya tverdykh tel, IL, M., 1956

[2] M. Bosterli, M. Rich, W. M. Visscher, “Simulation of nonharmonic interactions in a crystal by self-consistent reservoirs”, Phys. Rev. A, 1:4 (1970), 1086–1088 | DOI

[3] F. Bonetto, J. L. Lebowitz, J. Lukkarinen, “Fourier's law for a harmonic crystal with self- consistent stochastic reservoirs”, J. Stat. Phys., 116:1–4 (2004), 783–813, arXiv: math-ph/0307035 | DOI | MR

[4] E. Pereira, R. Falcao, “Nonequilibrium statistical mechanics of anharmonic crystals with self-consistent stochastic reservoirs”, Phys. Rev. E, 70:4 (2004), 046105, 5 pp., arXiv: cond-mat/0406474 | DOI

[5] R. Falkao, A. Fransisko Neto, E. Pereira, “Analiticheskii podkhod k (an)garmonicheskim kristallicheskim tsepochkam s samosoglasovannymi stokhasticheskimi rezervuarami”, TMF, 156:1 (2008), 138–146 | DOI | DOI | MR | Zbl

[6] Z. Rieder, J. L. Lebowitz, E. Lieb, “Properties of a harmonic crystal in a stationary nonequilibrium state”, J. Math. Phys., 8:5 (1967), 1073–1078 | DOI

[7] E. Pereira, H. C. F. Lemos, R. Ávila, “Ingredients of thermal rectification: The case of classical and quantum self-consistent harmonic chains of oscillators”, Phys. Rev. E, 84:6 (2011), 061135, 7 pp. | DOI

[8] F. Bonetto, J. L. Lebowitz, J. Lukkarinen, S. Olla, “Heat conduction and entropy production in anharmonic crystals with self-consistent stochastic reservoirs”, J. Stat. Phys., 134:5–6 (2009), 1097–1119, arXiv: 0809.0953 | DOI | MR

[9] E. Pereira, “Requisite ingredients for thermal rectification”, Phys. Rev. E, 96:1 (2017), 012114, 7 pp. | DOI

[10] A. Casher, J. L. Lebowitz, “Heat flow in regular and disordered harmonic chains”, J. Math. Phys., 12:8 (1971), 1701–1711 | DOI

[11] B. Øksendal, Stochastic Differential Equations. An Introduction with Applications, Springer, Berlin, 2003 | DOI | MR

[12] E. Pereira, L. M. Santana, R. Ávila, “Heat-flow properties of systems with alternate masses or alternate on-site potentials”, Phys. Rev. E, 84:1 (2011), 011116, 6 pp. | DOI

[13] B. Simon, “Notes on infinite determinants of Hilbert space operators”, Adv. Math., 24:3 (1977), 244–273 | DOI | MR

[14] B. Hu, L. Yang, Y. Zhang, “Asymmetric heat conduction in nonlinear lattices”, Phys. Rev. Lett., 97:12 (2006), 124302, 4 pp., arXiv: cond-mat/0511229 | DOI

[15] K. V. Reich, “Temperature gradient and Fourier's law in gradient-mass harmonic systems”, Phys. Rev. E, 87:5 (2013), 052109, 4 pp., arXiv: 1302.0478 | DOI

[16] E. Pereira, “Graded anharmonic crystals as genuine thermal diodes: Analytical description of rectification and negative differential thermal resistance”, Phys. Rev. E, 82:4 (2010), 040101, 4 pp., arXiv: 1101.4589 | DOI

[17] J. Wang, E. Pereira, G. Casati, “Thermal rectification in graded materials”, Phys. Rev. E, 86:1 (2012), 010101, 4 pp., arXiv: 1207.1169 | DOI

[18] E. Pereira, “Sufficient conditions for thermal rectification in general graded materials”, Phys. Rev. E, 83:3 (2011), 031106, 4 pp., arXiv: ; R. R. Ávila, E. Pereira, “Thermal rectification features: a study starting from local assumptions”, J. Phys. A: Math. Theor., 46:5 (2013), 055002, 13 pp. 1101.4590 | DOI | DOI | MR

[19] E. Pereira, “Graded anharmonic crystals as genuine thermal diodes: Analytical description of rectification and negative differential thermal resistance”, Phys. Rev. E, 82:4 (2010), 040101, 4 pp., arXiv: 1101.4589 | DOI

[20] E. Pereira, R. R. Ávila, “Increasing thermal rectification: Effects of long-range interactions”, Phys. Rev. E, 88:3 (2013), 032139, 6 pp., arXiv: 1309.4723 | DOI