R. Falcao, A. Francisco Neto, E. Pereira, “Analytic approach to the (an)harmonic crystal chains with self-consistent stochastic reservoirs”, TMF, 156:1 (2008), 138–146; Theoret. and Math. Phys., 156:1 (2008), 1081

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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 156, Number 1, Pages 138–146
DOI: https://doi.org/10.4213/tmf6235 (Mi tmf6235)

This article is cited in 15 scientific papers (total in 15 papers)

Analytic approach to the (an)harmonic crystal chains with self-consistent stochastic reservoirs

R. Falcao^a, A. Francisco Neto^b, E. Pereira^c

^a Centro de Formação de Professores, Universidade Federal do Reconcavo da Bahia
^b Núcleo de Física, Universidade Federal de Sergipe
^c Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais

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DOI: https://doi.org/10.4213/tmf6235

Abstract: We consider the harmonic and anharmonic chains of oscillators with self-consistent stochastic reservoirs and derive an integral representation (à la Feynman–Kac) for the correlations, in particular, for the heat flow. For the harmonic chain, we give a new proof that its thermal conductivity is finite in the steady state. Based on this integral representation for the correlations and a perturbative analysis, the approach is quite general and can be extended to more intricate systems.

Keywords: harmonic crystal, anharmonic crystal, stochastic reservoirs, heat flow.

Received: 22.06.2007

English version:
Theoretical and Mathematical Physics, 2008, Volume 156, Issue 1, Pages 1081–1088
DOI: https://doi.org/10.1007/s11232-008-0100-1

Bibliographic databases:

Language: Russian

Citation: R. Falcao, A. Francisco Neto, E. Pereira, “Analytic approach to the (an)harmonic crystal chains with self-consistent stochastic reservoirs”, TMF, 156:1 (2008), 138–146; Theoret. and Math. Phys., 156:1 (2008), 1081–1088

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https://www.mathnet.ru/eng/tmf6235

https://doi.org/10.4213/tmf6235

https://www.mathnet.ru/eng/tmf/v156/i1/p138

This publication is cited in the following 15 articles:

Humberto C F Lemos, Emmanuel Pereira, “Heat current properties of a rotor chain type model with next-nearest-neighbor interactions”, J. Phys. A: Math. Theor., 57:21 (2024), 215001
S. H. C. Silva, “Effective classical harmonic crystal with thermal rectification”, Theoret. and Math. Phys., 204:1 (2020), 918–926
Emmanuel Pereira, “Thermal rectification in classical and quantum systems: Searching for efficient thermal diodes”, EPL, 126:1 (2019), 14001
Emmanuel Pereira, “Requisite ingredients for thermal rectification”, Phys. Rev. E, 96:1 (2017)
Avila R.R., Pereira E., Teixeira D.L., “Length Dependence of Heat Conduction in (An)Harmonic Chains With Asymmetries Or Long Range Interparticle Interactions”, Physica A, 423 (2015), 51–60
Mendonca M.S., Pereira E., “Effective Approach For Anharmonic Chains of Oscillators: Analytical Description of Negative Differential Thermal Resistance”, Phys. Lett. A, 379:36 (2015), 1983–1989
Emmanuel Pereira, Mateus S Mendonça, Humberto C F Lemos, “Heat flow in anharmonic crystals with internal and external stochastic baths: a convergent polymer expansion for a model with discrete time and long range interparticle interaction”, J. Phys. A: Math. Theor., 48:37 (2015), 375203
Pereira E., Avila R.R., “Increasing Thermal Rectification: Effects of Long-Range Interactions”, Phys. Rev. E, 88:3 (2013), 032139
Saaskilahti K., Oksanen J., Tulkki J., “Thermal Balance and Quantum Heat Transport in Nanostructures Thermalized by Local Langevin Heat Baths”, Phys. Rev. E, 88:1 (2013), 012128
Pereira E., Lemos H.C.F., Avila R.R., “Ingredients of thermal rectification: The case of classical and quantum self-consistent harmonic chains of oscillators”, Phys Rev E, 84:6, Part 1 (2011), 061135
Pereira E., “Nontrivial properties of heat flow: Analytical study of some anharmonic lattice microscopic models”, Physica a-Statistical Mechanics and its Applications, 390:23–24 (2011), 4131–4143
Pereira E., Solha R.B., “Some properties of the thermal conductivity of chains of oscillators”, Phys. Rev. E, 81:6 (2010), 062101, 4 pp.
Pereira E., Lemos H.C.F., “Symmetry of heat conductivity in inhomogeneous quantum chains”, J. Phys. A, 42:22 (2009), 225006, 9 pp.
Pereira E., “Approximative analytical method for some Langevin dynamical systems”, Phys. A, 388:22 (2009), 4695–4702
Pereira E., Lemos H.C.F., “Symmetry properties of heat conduction in inhomogeneous materials”, Phys. Rev. E (3), 78:3 (2008), 031108, 6 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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