Keywords: heat flux, harmonic model.
@article{TMF_2020_204_1_a5,
author = {S. H. C. Silva},
title = {Effective classical harmonic crystal with thermal rectification},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {95--105},
year = {2020},
volume = {204},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2020_204_1_a5/}
}
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